Choosing the Optimal Product Mix with a Constrained Resource and a Demand Constraint
Billings Company produces two products, Product Reno and Product Tahoe. Each product goes through its own assembly and finishing departments. However, both of them must go through the painting department. The painting department has capacity of 2,460 hours per year. Product Reno has a unit contribution margin of $120 and requires 5 hours of painting department time. Product Tahoe has a unit contribution margin of $75 and requires 3 hours of painting department time. There are no other constraints.
Assume that only 500 units of each product can be sold.
Required:
1. What is the optimal mix of products?
| Optimal Mix | |
| Reno | units |
| Tahoe | units |
2. What is the total contribution margin earned
for the optimal mix?
$
| Reno | Tahoe | |
| Unit contribution margin (A) | $120 | $75 |
| Deparment hours required | 5 hours | 3 hours |
| Contribution margin per hour of painting department (B) | $ 24 | $ 25 |
| Since Tahoe has the Maximum Contribution margin, all department machine hours will be used for 500 units sold | ||
| Optimal Mix | ||
| Tahoe | 500 units | |
|
Reno (2,460 (-) (500 x $3) )/ 5 |
192 units | |
| Optimal Mix | ||
|
Tahoe (500 units x $75) |
$37,500 | |
|
Reno (192 units x $120) |
$23,040 | |
| Total Contribution Margin | $60,540 |
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