Question

PRODUCT MIX DECISION, SINGLE CONSTRAINT

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

• When there is a limiting factor, that product will be given preference that has the maximum contribution margin with respect to that ‘limiting factor’.
• In our case, the limiting factor is machine hours that are limited to 15000 hours.
• Requirement 1

Ranking of preference to produce or sell

	Basic	Standard	Deluxe
Selling price per unit	9	30	35
(-) Variable cost per unit	6	20	10
Contribution margin per unit	$3	$10	$25
Machine hour required per unit	0.1	0.5	0.75
Contribution margin per machine hours	$30	$20	$33.33
Ranking to produce and sell	2nd	3rd	1st

Since Deluxe product has maximum contribution per machine hour, all 15000 machine hours will be used to produce Deluxe to maximise the contribution.

Product Mix and total contribution margin---

Total machine hours available	15000 machine hours
Units of Deluxe that can be produced [15000 / 0.75 hours]	20000 units
Contribution margin per unit	$25
Total contribution margin [2000 x 25]	$500,000

• Requirement 2:

Now that Deluxe demand is restricted to 12000 units, all 15000 hours will not be used to produce ‘Deluxe’. Now the production will be as per ‘ranking’ done in working above.

Maximum demands for Delux model [given]	12000 units
Machine hours required for above [12000 x 0.75]	9000 hours
Remaining available machine hours for Basic and Standard [15000 – 9000]	6000 hours
Demand for Basic model [given]	50000 units
Machine hours required for above [50000 x 0.1]	5000 hours
Remaining available machine hours for Standard [6000 – 5000]	1000 hours
Units of Standard that can be produced [1000 / 0.5]	2000 units

Product Mix and total contribution margin

	Basic	Standard	Deluxe	Total
Units to be produced/sold	50000	2000	12000	64000 units
Machine hours per unit	0.1	0.5	0.75
Total machine hours	5000	1000	9000	15000 machine hours
Contribution margin per unit	$3	$10	$25
Total contribution margin	$150000	$20000	$300000	$470000