Question

2) A furniture store has set aside 800 square feet to display its sofas and chairs. Each sofa utilizes 50 sq. ft. and each chair utilizes 30 sq. ft. At least five sofas and at least five chairs are to be displayed.

A) Write a mathematical model representing the store's constraints.

B) Suppose the profit on sofas is $200 and on chairs is $100. On a given day, the probability that a displayed sofa will be sold is .03 and that a displayed chair will be sold is .05. Mathematically model each of the following objectives:

C) Maximize the total pieces of furniture displayed.

D) Maximize the total expected number of daily sales.

E) Maximize the total expected daily profit.

Answer 1

2)

Let

X = number of sofas

Y = number of chairs

A)

The constraint can be written as

50X + 30Y <= 800

B)

This means the expected profit is 0.03*200 = 6 for sofas and 0.05*100 = 5 for chairs.

C)

Maximize X + Y

D)

Maximize 0.03X + 0.05Y

E)

Maximize 6X + 5Y