Clay Corporation manufactures two styles of lamps-a Bedford Lamp and a Lowell Lamp. The following per unit data are available: Total fixed costs are $30,000. Marketing data indicate that the company can sell up to 8,000 units of the Bedford lamp and up to 4,000 units of the Lowell lamp. Machine hour capacity is 25,000 hours per year. What product mix will deliver the optimum operating income?

Question

Clay Corporation manufactures two styles of lamps-a Bedford Lamp and a Lowell Lamp. The following per unit data are available:  Total fixed costs are $30,000. Marketing data indicate that the company can sell up to 8,000 units of the Bedford lamp and up to 4,000 units of the Lowell lamp. Machine hour capacity is 25,000 hours per year. What product mix will deliver the optimum operating income?

Quizplus · Accepted Answer

To find the optimal product mix, we need to calculate the contribution margin per machine hour for each product:

Bedford Lamp: $70 - $45 = $25 contribution margin per unit / 2 machine hours = $12.50 contribution margin per machine hour
Lowell Lamp: $90 - $55 = $35 contribution margin per unit / 3 machine hours = $11.67 contribution margin per machine hour

Since the contribution margin per machine hour is higher for the Bedford Lamp, we should produce more of that product. However, we also need to consider the marketing data and machine hour capacity.

If we produce all Bedford Lamps (12,500 units), we will exceed our marketing potential and be left with excess inventory. Therefore, we need to produce some amount of Lowell Lamps as well.

Using linear programming, we can calculate that the optimal product mix is:
8,000 Bedford lamps and 2,250 Lowell lamps

This product mix will utilize 24,750 machine hours, which is within our machine hour capacity. It will also maximize our operating income, which can be calculated as:

8,000 Bedford lamps x $25 contribution margin per unit = $200,000
2,250 Lowell lamps x $35 contribution margin per unit = $78,750
Total contribution margin = $278,750
Total fixed costs = $30,000
Operating income = $248,750

Therefore, the best choice is C.

Clay Corporation Manufactures Two Styles of Lamps-A Bedford Lamp and a Lowell