Problem 13-45 Product Mix Decision, Single Constraint Sealing Company manufactur
ID: 3125334 • Letter: P
Question
Problem 13-45 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’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?
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
Explanation / Answer
Contribution Margin = Sales - Variable cost
We need to maximize the contibution margin.
Let the decision variables be:
x1 = Number of Basic storage units
x2 = Number of standard units
x3 = Number of deluxe units
We need to maximize = (9-6)*x1 + (30-20)*x2 + (35-10)*x3
Constraints:
0.10*x1 + 0.50*x2 + 0.75*x3 <= 15,000
Solving the LPP in excel, we get
x1 = 0
x2 = 0
x3 = 20000
(Contribution Margin)max = $500,000
2.) This will add three more constraints
x3 <= 12000
x1 <= 50000
x2 <= 50000
Again solving LPP using Excel
x1 = 3396
x2 = 11,320
x3 = 12,000
(Contribution Margin)max = $423,396