Description
Accounting assignment that contains 4 questions I uplthe subject book and the assignment fileAll answers should be clear and well presented with clear examples Please post your answers in the same file Avoid plagiarism so I don’t lose marks There must be at least two references All answers must be typed using Time new roman( size12, double-spaced)
Unformatted Attachment Preview
College of Administration and Finance Sciences
Assignment (2)
Deadline: Saturday 11/11/2023 @ 23:59
Course Name: Cost Accounting
Student’s Name:
Course Code: ACCT 301
Student’s ID Number:
Semester: 1st
CRN:
Academic Year: 1445 H
For Instructor’s Use only
Instructor’s Name:
Students’ Grade:
/15
Level of Marks: High/Middle/Low
Instructions – PLEASE READ THEM CAREFULLY
• The Assignment must be submitted on Blackboard (WORD format only) via allocated
folder.
• Assignments submitted through email will not be accepted.
• Students are advised to make their work clear and well presented, marks may be
reduced for poor presentation. This includes filling your information on the cover
page.
• Students must mention question number clearly in their answer.
• Late submission will NOT be accepted.
• Avoid plagiarism, the work should be in your own words, copying from students or
other resources without proper referencing will result in ZERO marks. No exceptions.
• All answers must be typed using Times New Roman (size 12, double-spaced) font.
No pictures containing text will be accepted and will be considered plagiarism.
• Submissions without this cover page will NOT be accepted.
College of Administration and Finance Sciences
Assignment Question(s):
(Marks 15)
Q1. Discuss with suitable examples why activity-based costing (ABC) is better than the
traditional costing system. Provide a suitable numerical example of ABC in the manufacturing
sector and show all the necessary calculations required under the ABC system.
(3 Marks)
Note: Your answer must include suitable numerical examples showing all the calculations of the
ABC system. You are required to assume values of numerical examples of your own and they should
not be copied from any sources.
(Chapter 7)
Answer:
Q2. “A non-routine decision is one that is taken in response to a non-repetitive, operational
scenario.” Comment on this statement and explain with suitable examples the various types of
non-routine operating decisions that a company makes under such a scenario. Support your
answer with numerical examples along with qualitative considerations involved in making such
decisions.
(4 Marks)
Note: Your answer must include suitable numerical examples for various types of non-routine
operating decisions. You are required to assume values of numerical examples of your own and they
should not be copied from any sources.
Answer:
(Chapter 4)
College of Administration and Finance Sciences
Q3. ADLG Company has two support departments, SS1 and SS2, and two operating
departments, OD1 and OD2. The company has decided to use the direct method and allocate
variable SS1 dept. costs based on the number of transactions and fixed SS1 dept. costs based on
the number of employees. SS2 dept. variable costs will be allocated based on the number of
service requests and fixed costs will be allocated based on the number of computers. The
following values have been extracted for the allocation:
(4 Marks)
Support Departments
Operating Departments
SS1
SS2
OD1
OD2
Total Department variable costs
16,000
19,000
105,000
68,000
Total department fixed costs
19,500
34,000
120,000
55,000
Number of transactions
50
55
250
140
Number of employees
18
24
47
38
Number of service requests
37
22
26
32
Number of computers
20
25
31
37
You are required to allocate variable and fixed costs.
(Chapter 8)
Answer:
Q4. JKL Company processes a direct material and produces three products: P1, P2, and P3. The
joint costs of the three products in 2018 were SAR 120,000. The total number of units for each
product and the selling price per unit is given below:
(4 Marks)
Product
Units
Selling Price per unit
P1
55,000
SAR 70
College of Administration and Finance Sciences
P2
34,500
SAR 58
P3
10,500
SAR 44
You are required to use the physical volume method and sales value at the split-off method to
allocate the joint costs to each product.
Answer:
(Chapter 9)
Cost Management
Measuring, Monitoring, and Motivating Performance
Chapter 4
Relevant Information for Decision Making
© John Wiley & Sons, 2011
Chapter 4: Relevant Costs for Nonroutine Operating Decisions
Eldenburg & Wolcott’s Cost Management, 2e
Slide # 1
Chapter 4: Relevant Costs for Nonroutine
Operating Decisions
Learning objectives
•
•
•
•
•
•
Q1: What is the process for identifying and using relevant
information in decision making?
Q2: How is relevant quantitative and qualitative information used
in special order decisions?
Q3: How is relevant quantitative and qualitative information used
in keep or drop decisions?
Q4: How is relevant quantitative and qualitative information used in
outsourcing (make or buy) decisions?
Q5: How is relevant quantitative and qualitative information used in
product emphasis and constrained resource decisions?
Q6: What factors affect the quality of operating decisions?
© John Wiley & Sons, 2011
Chapter 4: Relevant Costs for Nonroutine Operating Decisions
Eldenburg & Wolcott’s Cost Management, 2e
Slide # 2
Q1: Nonroutine Operating Decisions
• Routine operating decisions are those made on a
regular schedule. Examples include:
• annual budgets and resource allocation decisions
• monthly production planning
• weekly work scheduling issues
• Nonroutine operating decisions are not made on a
regular schedule. Examples include:
• accept or reject a customer’s special order
• keep or drop business segments
• insource or outsource a business activity
• constrained (scarce) resource allocation issues
© John Wiley & Sons, 2011
Chapter 4: Relevant Costs for Nonroutine Operating Decisions
Eldenburg & Wolcott’s Cost Management, 2e
Slide # 3
Q1: Nonroutine Operating Decisions
© John Wiley & Sons, 2011
Chapter 4: Relevant Costs for Nonroutine Operating Decisions
Eldenburg & Wolcott’s Cost Management, 2e
Slide # 4
Q1: Process for Making Nonroutine
Operating Decisions
1. Identify the type of decision to be made.
2. Identify the relevant quantitative analysis technique
(s).
3. Identify and analyze the qualitative factors.
4. Perform quantitative and/or qualitative analyses
5. Prioritize issues and arrive at a decision.
© John Wiley & Sons, 2011
Chapter 4: Relevant Costs for Nonroutine Operating Decisions
Eldenburg & Wolcott’s Cost Management, 2e
Slide # 5
Q1: Identify the Type of Decision
•
•
Special order decisions
•
determine the pricing
•
accept or reject a customer’s proposal for order quantity
and pricing
•
identify if there is sufficient available capacity
Keep or drop business segment decisions
•
examples of business segments include product lines,
divisions, services, geographic regions, or other distinct
segments of the business
•
eliminating segments with operating losses will not
always improve profits
© John Wiley & Sons, 2011
Chapter 4: Relevant Costs for Nonroutine Operating Decisions
Eldenburg & Wolcott’s Cost Management, 2e
Slide # 6
Q1: Identify the Type of Decision
•
•
•
Outsourcing decisions
•
make or buy production components
•
perform business activities “in-house” or pay another
business to perform the activity
Constrained resource allocation decisions
•
determine which products (or business segments)
should receive allocations of scarce resources
•
examples include allocating scarce machine hours or
limited supplies of materials to products
Other decisions may use similar analyses
© John Wiley & Sons, 2011
Chapter 4: Relevant Costs for Nonroutine Operating Decisions
Eldenburg & Wolcott’s Cost Management, 2e
Slide # 7
Q1: Identify and Apply the Relevant
Quantitative Analysis Technique(s)
•
•
Regression, CVP, and linear programming are
examples of quantitative analysis techniques.
Analysis techniques require input data.
•
Data for some input variables will be known and for
other input variables estimates will be required.
•
Many nonroutine decisions have a general
decision rule to apply to the data.
•
The results of the general rule need to be
interpreted.
•
The quality of the information used must be considered
when interpreting the results of the general rule.
© John Wiley & Sons, 2011
Chapter 4: Relevant Costs for Nonroutine Operating Decisions
Eldenburg & Wolcott’s Cost Management, 2e
Slide # 8
Q2-Q5 : Identify and Analyze Qualitative Factors
•
Qualitative information cannot easily be valued in
dollars.
•
•
•
can be difficult to identify
can be every bit as important as the quantitative
information
Examples of qualitative information that may be
relevant in some nonroutine decisions include:
•
quality of inputs available from a supplier
•
effects of decision on regular customers
•
effects of decision on employee morale
•
effects of production on the environment or the
community
© John Wiley & Sons, 2011
Chapter 4: Relevant Costs for Nonroutine Operating Decisions
Eldenburg & Wolcott’s Cost Management, 2e
Slide # 9
Q1: Consider All Information and Make a Decision
•
Before making a decision:
•
Consider all quantitative and qualitative information.
• Judgment is required when interpreting the effects of
qualitative information.
•
Consider the quality of the information.
• Judgment is also required when user lower-quality
information.
© John Wiley & Sons, 2011
Chapter 4: Relevant Costs for Nonroutine Operating Decisions
Eldenburg & Wolcott’s Cost Management, 2e
Slide # 10
Q2: Special Order Decisions
•
•
A new customer (or an existing customer) may
sometimes request a special order with a lower
selling price per unit.
The general rule for special order decisions is:
•
•
accept the order if incremental revenues exceed
incremental costs,
subject to qualitative considerations.
Price >= Relevant
Variable Costs +
•
Relevant
Fixed Costs +
Opportunity
Cost
If the special order replaces a portion of normal
operations, then the opportunity cost of accepting
the order must be included in incremental costs.
© John Wiley & Sons, 2011
Chapter 4: Relevant Costs for Nonroutine Operating Decisions
Eldenburg & Wolcott’s Cost Management, 2e
Slide # 11
Q2: Special Order Decisions
RobotBits, Inc. makes sensory input devices for robot manufacturers.
The normal selling price is $38.00 per unit. RobotBits was approached
by a large robot manufacturer, U.S. Robots, Inc. USR wants to buy
8,000 units at $24, and USR will pay the shipping costs. The per-unit
costs traceable to the product (based on normal capacity of 94,000
units) are listed below. Which costs are relevant to this decision?
yes
yes
yes
no
yes
no
no
no
© John Wiley & Sons, 2011
Relevant?
Relevant?
Relevant?
Relevant?
Relevant?
Relevant?
Relevant?
Chapter 4: Relevant Costs for Nonroutine Operating Decisions
Eldenburg & Wolcott’s Cost Management, 2e
$20.00
Slide # 12
Q2: Special Order Decisions
Suppose that the capacity of RobotBits is 107,000 units and projected
sales to regular customers this year total 94,000 units. Does the
quantitative analysis suggest that the company should accept the
special order?
First determine if there is sufficient idle capacity to accept this
order without disrupting normal operations:
Projected sales to regular customers
Special order 8,000 units
102,000
units
94,000 units
RobotBits still has 5,000 units of idle capacity if the order is
accepted. Compare incremental revenue to incremental cost:
Incremental profit if accept special order =
($24 selling price – $20 relevant costs) x 8,000 units = $32,000
© John Wiley & Sons, 2011
Chapter 4: Relevant Costs for Nonroutine Operating Decisions
Eldenburg & Wolcott’s Cost Management, 2e
Slide # 13
Q2: Qualitative Factors in
Special Order Decisions
What qualitative issues, in general, might RobotBits consider before
finalizing its decision?
• Will USR expect the same selling price per unit on future
orders?
• Will other regular customers be upset if they discover the
lower selling price to one of their competitors?
• Will employee productivity change with the increase in
production?
• Given the increase in production, will the incremental costs
remain as predicted for this special order?
• Are materials available from its supplier to meet the increase
in production?
© John Wiley & Sons, 2011
Chapter 4: Relevant Costs for Nonroutine Operating Decisions
Eldenburg & Wolcott’s Cost Management, 2e
Slide # 14
Q2: Special Order Decisions and Capacity Issues
Suppose instead that the capacity of RobotBits is 100,000 units and
projected sales to regular customers this year totals 94,000 units.
Should the company accept the special order?
Here the company does not have enough idle
capacity to accept the order:
Projected sales to regular customers
Special order 8,000 units
102,000
units
94,000 units
If USR will not agree to a reduction of the order to 6,000
units, then the offer can only be accepted by denying sales
of 2,000 units to regular customers.
© John Wiley & Sons, 2011
Chapter 4: Relevant Costs for Nonroutine Operating Decisions
Eldenburg & Wolcott’s Cost Management, 2e
Slide # 15
Q2: Special Order Decisions and Capacity Issues
Suppose instead that the capacity of RobotBits is 100,000 units and
projected sales to regular customers this year total 94,000 units. Does
the quantitative analysis suggest that the company should accept the
special order?
Variable cost/unit for
regular sales = $22.50.
CM/unit on regular sales
= $38.00 – $22.50 = $15.50.
The opportunity cost of accepting this
order is the lost contribution margin on
2,000 units of regular sales.
Incremental profit if accept special order =
$32,000 incremental profit under idle capacity – opportunity cost =
$32,000 – $15.50 x 2,000 = $1,000
© John Wiley & Sons, 2011
Chapter 4: Relevant Costs for Nonroutine Operating Decisions
Eldenburg & Wolcott’s Cost Management, 2e
Slide # 16
Q2: Qualitative Factors in
Special Order Decisions
What additional qualitative issues, in this case of a capacity constraint,
might RobotBits consider before finalizing its decision?
• What will be the effect on the regular customer(s) that do not
receive their order(s) of 2,000 units?
• What is the effect on the company’s reputation of leaving
orders from regular customers of 2,000 units unfilled?
• Will any of the projected costs change if the company
operates at 100% capacity?
• Are there any methods to increase capacity? What effects do
these methods have on employees and on the community?
• Notice that the small incremental profit of $1,000 will probably
be outweighed by the qualitative considerations.
© John Wiley & Sons, 2011
Chapter 4: Relevant Costs for Nonroutine Operating Decisions
Eldenburg & Wolcott’s Cost Management, 2e
Slide # 17
Q3: Keep or Drop Decisions
•
Managers must determine whether to keep or
eliminate business segments that appear to be
unprofitable.
•
The general rule for keep or drop decisions is:
•
•
keep the business segment if its contribution margin
covers its avoidable fixed costs,
subject to qualitative considerations.
Drop if: Contribution < Relevant
Margin
Fixed Costs +
•
Opportunity
Cost
If the business segment’s elimination will affect
continuing operations, the opportunity costs of its
discontinuation must be included in the analysis.
© John Wiley & Sons, 2011
Chapter 4: Relevant Costs for Nonroutine Operating Decisions
Eldenburg & Wolcott’s Cost Management, 2e
Slide # 18
Q3: Keep or Drop Decisions
Starz, Inc. has 3 divisions. The Gibson and Quaid Divisions have recently
been operating at a loss. Management is considering the elimination of these
divisions. Divisional income statements (in 1000s of dollars) are given below.
According to the quantitative analysis, should Starz eliminate Gibson or
Quaid or both?
© John Wiley & Sons, 2011
Chapter 4: Relevant Costs for Nonroutine Operating Decisions
Eldenburg & Wolcott’s Cost Management, 2e
Slide # 19
Q3: Keep or Drop Decisions
Use the general rule
to determine if Gibson
and/or Quaid should
be eliminated.
The general rule shows that we should keep Quaid and drop Gibson.
© John Wiley & Sons, 2011
Chapter 4: Relevant Costs for Nonroutine Operating Decisions
Eldenburg & Wolcott’s Cost Management, 2e
Slide # 20
Q3: Keep or Drop Decisions
Using the general rule is easier
than recasting the income
statements:
Quaid &
Russell
only
Profits increase by $11 when Gibson is eliminated.
© John Wiley & Sons, 2011
Chapter 4: Relevant Costs for Nonroutine Operating Decisions
Eldenburg & Wolcott’s Cost Management, 2e
Slide # 21
Q3: Keep or Drop Decisions
Suppose that the Gibson & Quaid Divisions use the same supplier for a
particular production input. If the Gibson Division is dropped, the decrease in
purchases from this supplier means that Quaid will no longer receive volume
discounts on this input. This will increase the costs of production for Quaid by
$14,000 per year. In this scenario, should Starz still eliminate the Gibson
Division?
Profits decrease by $3 when Gibson is eliminated.
© John Wiley & Sons, 2011
Chapter 4: Relevant Costs for Nonroutine Operating Decisions
Eldenburg & Wolcott’s Cost Management, 2e
Slide # 22
Q3: Qualitative Factors in
Keep or Drop Decisions
What qualitative issues should Starz consider before finalizing its
decision?
• What will be the effect on the customers of Gibson if it
is eliminated? What is the effect on the company’s
reputation?
• What will be the effect on the employees of Gibson?
Can any of them be reassigned to other divisions?
• What will be the effect on the community where Gibson
is located if the decision is made to drop Gibson?
• What will be the effect on the morale of the employees
of the remaining divisions?
© John Wiley & Sons, 2011
Chapter 4: Relevant Costs for Nonroutine Operating Decisions
Eldenburg & Wolcott’s Cost Management, 2e
Slide # 23
•
Q4: Insource or Outsource
(Make or Buy) Decisions
Managers often must determine whether to
•
•
•
The general rule for make or buy decisions is:
•
•
make or buy a production input
keep a business activity in house or outsource the activity
choose the alternative with the lowest relevant
(incremental cost), subject to qualitative considerations
If the decision will affect other aspects of
operations, these costs (or lost revenues) must be
included in the analysis.
Outsource if: Cost to Outsource < Cost to Insource
Where:
© John Wiley & Sons, 2011
Cost to
Relevant Relevant Opportunity
Insource =
FC
+
VC
+
Cost
Chapter 4: Relevant Costs for Nonroutine Operating Decisions
Eldenburg & Wolcott’s Cost Management, 2e
Slide # 24
Q4: Make or Buy Decisions
Graham Co. currently of our main product manufactures a part called a
gasker used in the manufacture of its main product. Graham makes and
uses 60,000 gaskers per year. The production costs are detailed below.
An outside supplier has offered to supply Graham 60,000 gaskers per
year at $1.55 each. Fixed production costs of $30,000 associated with
the gaskers are unavoidable. Should Graham make or buy the gaskers?
The production costs per unit for manufacturing a gasker are:
yes
Relevant?
Direct materials
$0.65
Relevant?
yes
Direct labor 0.45
Variable manufacturing overhead yes 0.40 Relevant?
no
Relevant?
Fixed manufacturing overhead* 0.50
$2.00
*$30,000/60,000 units = $0.50/unit
$1.50
Advantage of “make” over “buy” = [$1.55 - $1.50] x 60,000 = $3,000
© John Wiley & Sons, 2011
Chapter 4: Relevant Costs for Nonroutine Operating Decisions
Eldenburg & Wolcott’s Cost Management, 2e
Slide # 25
Q4: Qualitative Factors in
Make or Buy Decisions
The quantitative analysis indicates that Graham should continue to
make the component. What qualitative issues should Graham
consider before finalizing its decision?
• Is the quality of the manufactured component superior
to the quality of the purchased component?
• Will purchasing the component result in more timely
availability of the component?
• Would a relationship with the potential supplier benefit
the company in any way?
• Are there any worker productivity issues that affect this
decision?
© John Wiley & Sons, 2011
Chapter 4: Relevant Costs for Nonroutine Operating Decisions
Eldenburg & Wolcott’s Cost Management, 2e
Slide # 26
Q3: Make or Buy Decisions
Suppose the potential supplier of the gasker offers Graham a discount for a
different sub-unit required to manufacture Graham’s main product if Graham
purchases 60,000 gaskers annually. This discount is expected to save
Graham $15,000 per year. Should Graham consider purchasing the
gaskers?
Advantage of “make” over “buy”
before considering discount (slide 23)
$3,000
Discount
15,000
Advantage of “buy” over “make” $12,000
Profits increase by $12,000 when the gasker is purchased
instead of manufactured.
© John Wiley & Sons, 2011
Chapter 4: Relevant Costs for Nonroutine Operating Decisions
Eldenburg & Wolcott’s Cost Management, 2e
Slide # 27
Q5: Constrained Resource
(Product Emphasis) Decisions
•
Managers often face constraints such as
•
•
production capacity constraints such as machine hours
or limits on availability of material inputs
limits on the quantities of outputs that customers
demand
•
Managers need to determine which products
should first be allocated the scarce resources.
•
The general rule for constrained resource
allocation decisions with only one constraint is:
•
allocate scarce resources to products with the highest
contribution margin per unit of the constrained resource,
•
subject to qualitative considerations.
© John Wiley & Sons, 2011
Chapter 4: Relevant Costs for Nonroutine Operating Decisions
Eldenburg & Wolcott’s Cost Management, 2e
Slide # 28
Q5: Constrained Resource Decisions
(Two Products; One Scarce Resource)
Urban’s Umbrellas makes two types of patio umbrellas, regular and deluxe.
Suppose there is unlimited customer demand for each product. The selling
prices and variable costs of each product are listed below.
Regular
Deluxe
Selling price per unit
$40
$110
Variable cost per unit
20
44
Contribution margin per unit
$20
$ 66
Contribution margin ratio
50%
Required machine hours/unit
0.4
60%
2.0
Urban has only 160,000 machine hours available per year.
Write Urban’s machine hour constraint as an inequality.
0.4R + 2D ≤ 160,000 machine hours
© John Wiley & Sons, 2011
Chapter 4: Relevant Costs for Nonroutine Operating Decisions
Eldenburg & Wolcott’s Cost Management, 2e
Slide # 29
Q5: Constrained Resource Decisions
(Two Products; One Scarce Resource)
Suppose that Urban decides to make all Regular umbrellas. What is the total
contribution margin? Recall that the CM/unit for R is $20.
The machine hour constraint is: 0.4R + 2D ≤ 160,000 machine hours
If D=0, this constraint becomes 0.4R ≤ 160,000 machine hours,
or R ≤ 400,000 units
Total contribution margin = $20*400,000 = $8 million
Suppose that Urban decides to make all Deluxe umbrellas. What is the total
contribution margin? Recall that the CM/unit for D is $66.
If R=0, this constraint becomes 2D ≤ 160,000 machine hours, or
D ≤ 80,000 units
Total contribution margin = $66*80,000 = $5.28 million
© John Wiley & Sons, 2011
Chapter 4: Relevant Costs for Nonroutine Operating Decisions
Eldenburg & Wolcott’s Cost Management, 2e
Slide # 30
Q5: Constrained Resource Decisions
(Two Products; One Scarce Resource)
If the choice is between all Ds or all Rs, then clearly making all Rs
is better. But how do we know that some combination of Rs and Ds
won’t yield an even higher contribution margin?
make all Ds; get
$5.28 million
make all Rs; get
$8 million
In a one constraint problem, a combination of Rs and Ds will yield
a contribution margin between $5.28 and $8 million. Therefore,
Urban will only make one product, and clearly R is the best choice.
© John Wiley & Sons, 2011
Chapter 4: Relevant Costs for Nonroutine Operating Decisions
Eldenburg & Wolcott’s Cost Management, 2e
Slide # 31
Q5: Constrained Resource Decisions
(Two Products; One Scarce Resource)
The general rule for constrained resource decisions with one scarce
resource is to first make only the product with the highest
contribution margin per unit of the constrained resource.
In Urban’s case, the sole scarce resource was machine hours,
so Urban should make only the product with the highest
contribution margin per machine hour.
R: CM/mach hr = $20/0.4mach hrs = $50/mach hr
D: CM/mach hr = $66/2mach hrs = $33/mach hr
Notice that the total contribution margin from making all Rs
is $50/mach hr x 160,000 machine hours to be used
producing Rs = $8 million.
© John Wiley & Sons, 2011
Chapter 4: Relevant Costs for Nonroutine Operating Decisions
Eldenburg & Wolcott’s Cost Management, 2e
Slide # 32
Q5: Constrained Resource Decisions
(Multiple Scarce Resources)
•
Usually managers face more than one constraint.
•
Multiple constraints are easiest to analyze using a
quantitative analysis technique known as linear
programming.
•
A problem formulated as a linear programming
problem contains
•
an algebraic expression of the company’s goal, known
as the objective function
• for example “maximize total contribution margin” or “minimize
total costs”
•
a list of the constraints written as inequalities
© John Wiley & Sons, 2011
Chapter 4: Relevant Costs for Nonroutine Operating Decisions
Eldenburg & Wolcott’s Cost Management, 2e
Slide # 33
Q5: Constrained Resource Decisions
(Two Products; Two Scarce Resources)
Suppose Urban also need 2 and 6 hours of direct labor per unit of R
and D, respectively. There are only 120,000 direct labor hours available
per year. Formulate this as a linear programming problem.
Max 20R + 66D
R,D
subject to:
0.4R+2D ≤ 160,000 mach hr constraint
2R+6D ≤ 120,000 DL hr constraint
nonnegativity constraints
R≥0
(can’t make a negative
D≥0
amount of R or D)
objective function
R, D are the
choice variables
constraints
© John Wiley & Sons, 2011
Chapter 4: Relevant Costs for Nonroutine Operating Decisions
Eldenburg & Wolcott’s Cost Management, 2e
Slide # 34
Q5: Constrained Resource Decisions
(Two Products; Two Scarce Resources)
Draw a graph showing the possible production plans for Urban.
Every R, D ordered pair
To determine this, graph the
is a production plan.
constraints as inequalities.
But which ones are feasible,
0.4R+2D ≤ 160,000 mach hr constraint
given the constraints?
When D=0, R=400,000
D
When R=0, D=80,000
2R+6D ≤ 120,000 DL hr constraint
When D=0, R=60,000
When R=0, D=20,000
80,000
20,000
60,000
© John Wiley & Sons, 2011
400,000
R
Chapter 4: Relevant Costs for Nonroutine Operating Decisions
Eldenburg & Wolcott’s Cost Management, 2e
Slide # 35
Q5: Constrained Resource Decisions
(Two Products; Two Scarce Resources)
There are not enough machine hours or enough
direct labor hours to produce this production plan.
There are enough machine hours, but
not enough direct labor hours, to
produce this production plan.
This production plan is feasible;
there are enough machine hours
and enough direct labor hours for
this plan.
D
80,000
The feasible set is the area where all the
production constraints are satisfied.
20,000
60,000
© John Wiley & Sons, 2011
400,000
R
Chapter 4: Relevant Costs for Nonroutine Operating Decisions
Eldenburg & Wolcott’s Cost Management, 2e
Slide # 36
Q5: Constrained Resource Decisions
(Two Products; Two Scarce Resources)
The graph helped us realize an important aspect of this
problem – we thought there were 2 constrained resources but
in fact there is only one.
For every feasible production plan, Urban will never
run out of machine hours.
D
The machine hour constraint is non-binding, or slack,
but the direct labor hour constraint is binding.
80,000
We are back to a one-scarceresource problem.
20,000
60,000
© John Wiley & Sons, 2011
400,000
R
Chapter 4: Relevant Costs for Nonroutine Operating Decisions
Eldenburg & Wolcott’s Cost Management, 2e
Slide # 37
Q5: Constrained Resource Decisions
(Two Products; One Scarce Resource)
Here direct labor hours is the sole scarce resource.
We can use the general rule for one-constraint problems.
R: CM/DL hr = $20/2DL hrs = $10/DL hr
D: CM/DL hr = $66/6DL hrs = $11/DL hr
D
Urban should make all deluxe umbrellas.
80,000
Optimal plan is R=0, D=20,000.
Total contribution margin = $66 x
20,000 = $1,320,000
20,000
60,000
© John Wiley & Sons, 2011
400,000
R
Chapter 4: Relevant Costs for Nonroutine Operating Decisions
Eldenburg & Wolcott’s Cost Management, 2e
Slide # 38
Q5: Constrained Resource Decisions
(Two Products; Two Scarce Resources)
Suppose Urban has been able to train a new workforce and now there
are 600,000 direct labor hours available per year. Formulate this as a
linear programming problem, graph it, and find the feasible set.
Max 20R + 66D
R,D
subject to:
0.4R+2D ≤ 160,000 mach hr constraint
2R+6D ≤ 600,000
DL hr constraint
R≥0
D≥0
The formulation of the problem is the same as before; the
only change is that the right hand side (RHS) of the DL
hour constraint is larger.
© John Wiley & Sons, 2011
Chapter 4: Relevant Costs for Nonroutine Operating Decisions
Eldenburg & Wolcott’s Cost Management, 2e
Slide # 39
Q5: Constrained Resource Decisions
(Two Products; Two Scarce Resources)
The machine hour constraint is the same as before.
0.4R+2D ≤ 160,000 mach hr constraint
D
100,000
2R+6D ≤ 600,000 DL hr constraint
When D=0, R=300,000
When R=0, D=100,000
80,000
300,000
© John Wiley & Sons, 2011
400,000
R
Chapter 4: Relevant Costs for Nonroutine Operating Decisions
Eldenburg & Wolcott’s Cost Management, 2e
Slide # 40
Q5: Constrained Resource Decisions
(Two Products; Two Scarce Resources)
There are not enough machine hours or enough
direct labor hours for this production plan.
There are enough direct labor hours, but not
enough machine hours, for this production plan.
D
100,000
There are enough machine hours, but not
enough direct labor hours, for this production
plan.
This production plan is feasible; there
are enough machine hours and enough
direct labor hours for this plan.
80,000
The feasible set is the area where all the
production constraints are satisfied.
300,000
© John Wiley & Sons, 2011
400,000
R
Chapter 4: Relevant Costs for Nonroutine Operating Decisions
Eldenburg & Wolcott’s Cost Management, 2e
Slide # 41
Q5: Constrained Resource Decisions
(Two Products; Two Scarce Resources)
How do we know which of the feasible plans is optimal?
We can’t use the general rule for one-constraint problems.
We can graph the total contribution margin line, because its slope
will help us determine the optimal production plan.
D
100,000
80,000
The objective “maximize total
contribution margin” means that we
. . . this would be the
choose a production plan so that the
optimal production plan.
contribution margin is a large as
possible, without leaving the feasible
set. If the slope of the total contribution
margin line is lower (in absolute value
terms) than the slope of the machine
hour constraint, then. . .
300,000
© John Wiley & Sons, 2011
400,000
R
Chapter 4: Relevant Costs for Nonroutine Operating Decisions
Eldenburg & Wolcott’s Cost Management, 2e
Slide # 42
Q5: Constrained Resource Decisions
(Two Products; Two Scarce Resources)
What if the slope of the total contribution margin line is higher (in
absolute value terms) than the slope of the direct labor hour
constraint?
If the total CM line had this steep slope, . .
D
100,000
. . then this would
be the optimal
production plan.
80,000
300,000
© John Wiley & Sons, 2011
400,000
R
Chapter 4: Relevant Costs for Nonroutine Operating Decisions
Eldenburg & Wolcott’s Cost Management, 2e
Slide # 43
Q5: Constrained Resource Decisions
(Two Products; Two Scarce Resources)
What if the slope of the total contribution margin line is between
the slopes of the two constraints?
If the total CM line had this slope, . .
D
100,000
. . then this would
be the optimal
production plan.
80,000
300,000
© John Wiley & Sons, 2011
400,000
R
Chapter 4: Relevant Costs for Nonroutine Operating Decisions
Eldenburg & Wolcott’s Cost Management, 2e
Slide # 44
Q5: Constrained Resource Decisions
(Two Products; Two Scarce Resources)
The last 3 slides showed that the optimal production plan is always
at a corner of the feasible set. This gives us an easy way to solve
2 product, 2 or more scarce resource problems.
D
100,000
R=0, D=80,000
The total contribution margin here is
0 x $20 + 80,000 x $66 = $5,280,000.
R=?, D=?
Find the intersection of the 2 constraints.
80,000
R=300,000, D=0
The total contribution margin here is
300,000 x $20 + 0 x $66 = $6,000,000.
300,000
© John Wiley & Sons, 2011
400,000
R
Chapter 4: Relevant Costs for Nonroutine Operating Decisions
Eldenburg & Wolcott’s Cost Management, 2e
Slide # 45
Q5: Constrained Resource Decisions
(Two Products; Two Scarce Resources)
To find the intersection of the 2 constraints, use substitution or
subtract one constraint from the other.
multiply each side by 5
Total CM = $5,280,000.
D
100,000
80,000
0.4R+2D = 160,000 2R+10D = 800,000
2R+6D = 600,000
2R+6D = 600,000
subtract 0R+4D = 200,000
D = 50,000
Total CM = $20 x 150,000 +
2R+6(50,000) = 600,000
$66 x 50,000 = $6,300,000.
2R = 300,000
R = 150,000
Total CM = $6,000,000.
300,000
© John Wiley & Sons, 2011
400,000
R
Chapter 4: Relevant Costs fo
