Question

The logistics/operations manager of a mail-order house purchases two products for resale: King Beds (X) and Queen Beds (Y). Each King bed costs $500 and requires 100 cubic feet of storage space, and each Queen Bed costs $300 and requires 90 cubic feet of storage space. The manager has $75,000 to invest in beds this week, and her warehouse has 18,000 cubic feet available for storage. Profit for each King Bed is $300 and for each Queen Bed is $150. The objective is to maximize profits. Convert this word problem into an LP model and then SOLVE it using the graphical solution method. Note: You MUST solve Problem 1 using the graphical solution method and show all your algebra just like in the adobe file I had sent you last week - in order to get full credit.

Answer 1

LP model is formulated as below:

Max 300X+150Y

s.t.

500X+300Y <= 75000 (total budget this week)

100X+90Y <= 18000 (total storage space available in warehouse)

X, Y >= 0

Solution using graphical method is following:

Optimal solution:

Number of Kings Beds (X) to be purchased for resale = 150

Number of Queens Beds (Y) to be purchased for resale = 0

Total profit = $ 45,000