Constrained Optimization: One Internal Binding Constraint
Patz Company produces two types of machine parts: Part A and Part B, with unit contribution margins of $500 and $1,000, 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 500 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 = $500 A + $1,000 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 125 units of Part A and 100 units of Part B? Express the objective function with its associated constraints for this case.
Objective function: Max Z = $500 A + $1,000 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. $