PRODUCT MIX DECISION, SINGLE CONSTRAINT Sealing Company manufactures three types
ID: 2544870 • Letter: P
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?
Explanation / Answer
Answer
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
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
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
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