Cornerstones of Cost Accounting 1st Edition by Don Hansen,Maryanne Mowen

Exercise 4

CONSTRAINED OPTIMIZATION: ONE INTERNAL BINDING CONSTRAINT
Fisher Company produces two types of airplane components: Component A and Component B, with unit contribution margins of $200 and $400, respectively. Assume initially that Fisher can sell all that is produced of either component. Component 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 total contribution margin subject to the assembly-hour constraint.
2. Identify the optimal amount that should be produced of each airplane component and the total contribution margin associated with this mix.
3. What if market conditions are such that Fisher can sell at most 50 units of Component A and 40 units of Component B? Express the objective function with its associated constraints for this case and identify the optimal mix and its associated total contribution margin.