Constrained Optimization: One Internal Binding Constraint

Patz Company produces two types of machine parts: Part A and Part B, with unit contribution margins of $300 and $600, 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 300 assembly hours per week.

1.Express the objective of maximizing the total contribution margin subject to the assembly-hour constraint.

Objective function: MaxZ= $300A+ $600B

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 ifmarket conditions are such that Patz can sell at most 75 units of Part A and 60 units of Part B? Express the objective function with its associated constraints for this case.

Objective function:MaxZ= $300A+ $600B

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.

Component A $____________units

Component B $_____________units

Total contribution $______________