Cornerstone Exercise 20.3 (Algorithmic) Constrained Optimization: One Internal Binding Constraint

Patz Company produces two types of machine parts: Part A and Part B, with unit contribution margins of $200 and $400, 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 200 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 = $200 A + $400 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 50 units of Part A and 40 units of Part B? Express the objective function with its associated constraints for this case.

Objective function: Max Z = $200 A + $400 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. $