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 $400 and $800, 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 400 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 = $400 A + $800 B Subject to: 2 A+ 5 Bs 400 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 200 units Component B 0 units Identify the total contribution margin associated with this mix. 3. What if market conditions are such that Patz can sell at most 100 units of Part A and 80 units of Part B? Express the objective function with its associated constraints for this case. Objective function: Max Z = $400 A + $800 B Assembly-hour constraint Demand constraint for Part A A Demand constraint for Part B BS Identify the optimal mix and its associated total contribution margin. $ $