Question

Sealing Company manufactures three types of DVD storage units. Each of the three types requires 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:

Basic              Standard       Deluxe

Selling price                        $9.00              $30.00           $35.00

Variable cost                        $6.00              $20.00           $10.00

Machine hours required       0.10                 0.50                0.75

Sealing Company'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

	Basic	Standard	Deluxe
Selling price	9.00	30.00	35.00
Variable cost	6.00	20.00	10.00
Contribution margin per unit $	3.00	10.00	25.00
Machine hours required per unit	0.10	0.50	0.75
Contribution margin per machine hour $	30.00	20.00	33.33
Ranking	II	III	I
Number of units to be produced			20000
			(15000/0.75)

Since the contribution margin per machine hour is the highest for Deluxe type, entire 15000 machine hours should be utilized to produce the Deluxe type which will maximize the company's contribution margin. Thus, 20000 units of the Deluxe type should be produced and sold.

Total contribution margin = 20000 x $25 = $500000

	Basic	Standard	Deluxe
Contribution margin per unit $	3.00	10.00	25.00
Machine hours required per unit	0.10	0.50	0.75
Contribution margin per machine hour $	30.00	20.00	33.33
Ranking	II	III	I
Number of unit to be produced	50000	2000	12000
		(1000/0.50)
Machine hours required	5000	1000	9000
	(50000 x 0.10)	(Balance)	(12000 x 0.75)

The demand for the Deluxe type which has the highest contribution margin per machine hour should be fulfilled first. Next, the demand for the Basic type should be fulfilled and the remaining balance machine hours should lastly be used for producing the Standard type. Thus, 12000 units of Deluxe, 50000 units of Basic, and 2000 units of Standard type should be produced.

Total contribution margin:

Basic (50000 x $3)	150000
Standard (2000 x $10)	20000
Deluxe (12000 x $25)	300000
Total contribution margin $	470000