Master Buy Appliance Store must determine how many super screen TVs to keep in s
ID: 466009 • Letter: M
Question
Master Buy Appliance Store must determine how many super screen TVs to keep in stock. There are only two models, A and B. Model A requires 10 square feet of floor space, and model B requires 6 square feet of floor space; 5000 square feet of floor space is available for these TVs. Each Model A sale results in an $80 profit, while each model B sale results in a profit of $50. Marketing requirements dictate that at least 60% of the super screen TVs in stock be Model Bs.
Write the linear programming formulation for this problem
Explanation / Answer
Model A :
Floor Space - 10 sq. ft.
Profit - $80
Model B :
Floor Space - 6 sq. ft.
Profit - $50
Total space available for both the models A,B = 5000 sq. ft.
Marketing requirement = 60% of the super screen TV's in stock should be model B.
Let x = number of model - A Tv's
y = number of model - B Tv's
constraints; x > 0, y > 0
10x + 6y > 5000
s.t, 80x + 50y > 0
x > 0
y > 0
Marketing dictates that at least 60% of the TV's should be model B.
It means, number of model B TV's should be at least - 3000
Substitute values in the equation 10x + 6y > 5000
values that satisfy the equation are - (200, 500)
500 numbers of model B TV's will amount to a total of 3000 Model B TV's
200 numbers of model A TV's will amount to a total of 2000 Model A TV's
10(200) + 6(500) > 5000
Profit for Model A = 200 * 80 = $16000
Profit for Model B = 500 * 50 = $25000