1st part of problem

With 7 years of experience as a salesperson for a national retailer, John has decided to start his own business. He plans to sell designer clothing and has already found a convenient location in a large suburban shopping centre. The store will carry the goods of 4 well-known designers. John has decided that his inventory should not exceed $75,000.

John must decide how to allocate the floor space to the 4 brands he has decided to carry. Each

manufacturer requires that a minimum amount of floor space be allocated to its goods. The total surface of Johns store is 3,360 square feet.

The space requirements and some budgeted figures for the first year of operation are as follows:

Manufacturer #1 #2 #3 #4

Minimum floor space (square feet) 500 700 600 900

Expected annual sales ($ per square foot) 300 480 450 600

Average gross margin 40% 45% 38% 35%

The following are annual costs:

Salaries $100,000

Rent $40 per square foot

Utilities $4,500

Salaries, rent, and utilities are fixed costs.

To solve his problem, John has set up the following linear program:

Maximize: (M1, M2, M3, M4) = 108M1 + 187.2M2 + 153M3 + 192M4

Subject to:

M1 + M2 + M3 +M4 <= 3,360 Total floor space constraint

M1 > = 500 Minimum floor space for Manufacturer #1

M2 > = 700 Minimum floor space for Manufacturer #2

M3 > = 600 Minimum floor space for Manufacturer #3

M4 > = 900 Minimum floor space for Manufacturer #4

15M1 + 22M2 + 23.25M3 + 32.50M4 < = 75,000 Maximum inventory

Where:

M1 represents the number of square feet allocated to goods of manufacturer #1

M2 represents the number of square feet allocated to goods of manufacturer #2

M3 represents the number of square feet allocated to goods of manufacturer #3

M4 represents the number of square feet allocated to goods of manufacturer #4

The linear program was solved using Solver. The results are included in Exhibit 7-1.

I have posted the 2nd half of the problem won't let me paste anymore too long.