Choosing the Optimal Product Mix with One Constrained Resource Billings Company

Question

Choosing the Optimal Product Mix with One Constrained Resource

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 five hours of painting department time. Product Tahoe has a unit contribution margin of $75 and requires three hours of painting department time. There are no other constraints.

Required:

1. What is the contribution margin per hour of painting department time for each product? If required, round your answers to the nearest cent.

2. What is the optimal mix of products? If an amount is zero, enter "0".

3. What is the total contribution margin earned for the optimal mix?
$ ( )

Contribution Margin Reno $ ( ) Tahoe $ ( )

Explanation / Answer

SOLUTION

(A)

(B) Assuming no other constraints, the optimal mix is zero units of Reno and 820 units of Tahoe. Total painting department time is 2,460 hours per year; if all of them are devoted to Tahoe production, then 820 units (2,460/3) of Tahoe can be produced.

(C) Contribution margin = ($120 * $0) + ($75 * $820) = $61,500

Reno Tahoe Unit contribution margin (A) $120 $75 Painting department hours (B) 5 3 Contribution margin per unit scarce resource (A/B) $24 $25

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