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. $_____________________________-