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Constrained Optimization: One Internal Binding Constraint

Patz Company produces two types of machine parts: Part A and Part B, with unit contribution margins of $100 and $200, 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 100 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 = $100 A + $200 B

Subject to: fill in the blank 1 A + fill in the blank 2 B fill in the blank 3

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	fill in the blank 4	units
Component B	fill in the blank 5	units

Identify the total contribution margin associated with this mix. $fill in the blank 6

3. What if market conditions are such that Patz can sell at most 25 units of Part A and 20 units of Part B? Express the objective function with its associated constraints for this case.

Objective function: Max Z = $100 A + $200 B

Assembly-hour constraint	fill in the blank 7 A + fill in the blank 8 B fill in the blank 9
Demand constraint for Part A	A fill in the blank 10
Demand constraint for Part B	B fill in the blank 11

Identify the optimal mix and its associated total contribution margin. Component A $fill in the blank 12 units

Component B $fill in the blank 13 units

Total contribution $fill in the blank 14