Practical Management Science
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ISBN: 9781337406659
Author: WINSTON, Wayne L.
Publisher: Cengage,
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Constrained Optimization: One Internal Binding Constraint
Patz Company produces two types of machine parts: Part A and Part B, with unit contribution margins of $100 and $200, respectively. Assume initially that Patz can sell all that is produced of either component. Part A requires two hours of assembly, and B requires five hours of assembly. The firm has 100 assembly hours per week.
Required:
1. Express the objective of maximizing the total contribution margin subject to the assembly-hour constraint.
Objective function: Max Z = $100 A + $200 B
Subject to: fill in the blank 1 A + fill in the blank 2 B ≤ fill in the blank 3
2. Identify the optimal amount that should be produced of each machine part. If none of the components should be produced, enter "0" for your answer.
| Component A | fill in the blank 4 | units |
| Component B | fill in the blank 5 | units |
Identify the total contribution margin associated with this mix.
$fill in the blank 6
3. What if market conditions are such that Patz can sell at most 25 units of Part A and 20 units of Part B? Express the objective function with its associated constraints for this case.
Objective function: Max Z = $100 A + $200 B
| Assembly-hour constraint | fill in the blank 7 A + fill in the blank 8 B ≤ fill in the blank 9 |
| Demand constraint for Part A | A ≤ fill in the blank 10 |
| Demand constraint for Part B | B ≤ fill in the blank 11 |
Identify the optimal mix and its associated total contribution margin.
Component A $fill in the blank 12 units
Component B $fill in the blank 13 units
Total contribution $fill in the blank 14
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