The Apex Television Company has to decide on the number of 60- and 42- inch sets
ID: 3043445 • Letter: T
Question
The Apex Television Company has to decide on the number of 60- and 42- inch sets to be produces at one of its factories. Market research indicates that at most 40 of the 60-inch sets and 10 of the 42-inch sets ca be sold per month. The maximum number of workhours available is 500 per month. A 60-inch set required 20 work-hours and 42-inch set requires 10 work-hours. Each 60-inch set sold produces a profit of $120 and each 42-inch set produces a profit of $80. A wholesaler has agreed to purchase all the television sets produces if the numbers do not exceed the maxima indicated by the market research. Formulate a linear programming model for this problem and find the maximum profit of the company. Define the Variable. Formulate an OPL.
60-inch TV’s = x
42-inch TV’s = y
x 40, maximum 60-inch TV’s that can be produced.
y 10, maximum 42-inch TV’s that can be produced.
Based on the work hours per month:
20x + 10y 500 (available work hours)
10y 500 – 20x
y 50-2x
The profit function is:
Z= 120x + 80y = 3200
(0,0) = 0
(25,0) = 3,000
(0,10) = 800
(20,10) = 3,200
(20,10) is the maximum due to a $3,200 profit. They should produce 20 of the 60- inch TV’s and 10 of the 42-inch TV’s.
Explanation / Answer
60-inch TV’s = x
42-inch TV’s = y
x 40, maximum 60-inch TV’s that can be produced.
y 10, maximum 42-inch TV’s that can be produced.
Based on the work hours per month:
20x + 10y 500 (available work hours)
The profit function is:
Z= 120x + 80y
Tableau #1
x y s1 s2 s3 p
1 0 1 0 0 0 40
0 1 0 1 0 0 10
20 10 0 0 1 0 500
-120 -80 0 0 0 1 0
Tableau #2
x y s1 s2 s3 p
0 -0.5 1 0 -0.05 0 15
0 1 0 1 0 0 10
1 0.5 0 0 0.05 0 25
0 -20 0 0 6 1 3000
Tableau #3
x y s1 s2 s3 p
0 0 1 0.5 -0.05 0 20
0 1 0 1 0 0 10
1 0 0 -0.5 0.05 0 20
0 0 0 20 6 1 3200
Optimal Solution: p = 3200; x = 20, y = 10
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