A store in Rio Piedras has to make room for new outfits by l

A store in Rio Piedras has to make room for new outfits by liquidating 200 of its shirts and 100 pairs of pants from last season. They have decided to put together two offers, A and B. Offer A is a package of one shirt and a pair of pants which will sell for $30. Offer B is a package of three shirts and a pair of pants, which will sell for $50. The store does not want to sell less than 20 packages of Offer A and less than 10 of Offer B. At least 60% of the products have to be shirts. Formulate a LP model to determine how many packages of each do they have to sell to maximize the money generated from the promotion?

Solution

Choose the unknowns.

x = number of packages of Offer A

y = number of packages of Offer B

Write the objective function.

f(x, y) = 30x + 50y

x + 3y 200

x + y 100

x 20

y 10

Calculate the value of the objective function at each of the vertices to determine which of them has the maximum or minimum values.

f(x, y) = 30 · 20 + 50 · 10 = $1,100

f(x, y) = 30 · 90 + 50 · 10 = $3,200

f(x, y) = 30 · 20 + 50 · 60 = $3,600

f(x, y) = 30 · 50 + 50 · 50 = $4,000   Maximum

50 packages of each offer generates a maximum amount of $4,000 in sales.