Question

Having trouble trying to solve 8-62

Problem 8-62 Product Mix Decision, Single Constraint Scaling Company manufactures three types of DVD storage units. Each of the three types re- quires the use of a special machine that has a total operating capacity of 15,000 hours per year. Information on the three types of storage units is as follows: Selling price Variable cost Machine hours required Basic $9.00 $6.00 0.10 Standard $30.00 $20.00 0.50 Deluxe $35.00 $10.00 0.75 Sealing's marketing director has assessed demand for the three types of storage units and believes that the firm can sell as many units as it can produce. Required: 1. How many of each type of unit should be produced and sold to maximize the company's contribution margin? What is the total contribution margin for your selection? 2. Now suppose that Sealing Company believes that it can sell no more than 12,000 of the deluxe model but up to 50,000 each of the basic and standard models at the selling prices estimated. What product mix would you recommend, and what would be the total contribution margin?

Answer 1

Requirement 1

This question is based on limiting factor. The limiting factor here is machine hours i.e. 15000 machine hours, beyond which no production can be made. The contribution needs to be optimized within this hours.

	Basic	Standard	Deluxe
Price	$           9	$        30	$            35
Variable cost	6	20	10
Contribution margin (A)	3	10	25
Machine hours (B)	0.1	0.5	0.75
Contribution margin per machine hours (A/B)	$            30.00	$         20.00	$        33.33

Analyzing the above, the company shall only sell deluxe unit with contribution margin of $ 33.33 per machine hour. Sealing can produce 20,000 (15,000/0.75) deluxe units per year. These 20,000 units, multiplied by the $25 contribution margin per unit, would yield a total contribution margin of $500,000.

Requirement 2

First of all,12,000 deluxe units shall be produced and sold, using 9,000 machine hours. Then, produce and sell 50,000 basic units, which would use 5,000 machine hours. Finally, with the remaining 1,000 machine hours, produce 2,000 standard units.

Required product mix would be

Basic =50,000 units

Standard = 2,000 units &

Deluxe = 12,000 units

Total contribution margin= ($3 × 50,000) + ($25 × 12,000) + ($10 × 2,000) = $470,000

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