Question

Constrained Optimization: One Internal Binding Constraint

Patz Company produces two types of machine parts: Part A and Part B, with unit contribution margins of $300 and $600, 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 300 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 = $300 A + $600 B

Subject to:  A +  B ≤

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		units
Component B		units

Identify the total contribution margin associated with this mix.
$

3. What if market conditions are such that Patz can sell at most 75 units of Part A and 60 units of Part B? Express the objective function with its associated constraints for this case.

Objective function: Max Z = $300 A + $600 B

Assembly-hour constraint	A +  B ≤
Demand constraint for Part A	A ≤
Demand constraint for Part B	B ≤

Identify the optimal mix and its associated total contribution margin.
Component A $ units

Component B $ units

Total contribution $

Answer 1

1
Objective function:	Max Z = $300 A + $600 B
Subject to:	2 A + 3 B ≤ 300
2
Contribution margin per Unit
Component A	300/2 = 150
Component B	600/5 = 120
Optimal Amount
Component A	300*150 = 45,000
Component B	0
3
Assembly-hour constraint	2 A + 5 B ≤ 300
Demand constraint for Part A	A ≤ 75
Demand constraint for Part B	B ≤ 60
Component A (300*75)	$22,500
Component B (600*30)	$18,000
Total Contribution Margin	$40,500