Description
This is a solver question
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A manager wants to know how many units of each product to produce on a daily basis in order to
achieve the highest contribution to profit. Production resource and material requirements for the
products are shown in the following table.
Product
A
B
C
Material 1
(pounds)
Material 2
(pounds)
Labor
(hours)
Equipment
(hours)
2.5
3
4
3
5
0
2.5
1.4
1.75
2
1.6
1.5
Material 1 costs $8.50 a pound, material 2 costs $6.25 a pound, and labor costs $12 an hour.
Management considers equipment hours as overhead and chooses to not include it in product costing
(the wisdom of that decision is up for debate). Product A sells for $90 a unit, product B sells for $100 a
unit, and product C sells for $78 a unit. Available resources each day are 1200 pounds of material 1,
1,400 pounds of material 2, 1,000 hours of labor and 700 hours equipment time.
The manager must satisfy certain output requirements:
The output of product A should be at least ¼ of the total number of units produced
There is a standing order for 50 units of product B each day.
We can sell no more than 75 units of product C each day.
a. Formulate an LP model for this problem (i.e. the standard table format from PowerPoint and in
class.) Define your decision variables, create the objective function formula in terms of your
decision variables, and create and label your constraints. Just type this into Sheet 1 of your Excel
file in a text box or use Equation Editor. (3 points)
e.g. something like:
Decision Variables:
• x1 = the number of product X to make
• x2 = the number of product Y to make
• and so on . . . .
Constraints:
•
max 2 x1 + 3 x2 + x3 + 4×4
• subject to:
•
x1 + 3 x2 + 5 x3 + x4
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