Question

4)     Jaycee’s department store chain is planning to open a new store. It needs to decide how to allocate the 100,000 square feet of available floor space among seven departments. Data on expected performance of each department per month, in terms of square feet (sf), are shown next.

        

Department	Investment/sf	Risk as a % of $ invested	Minimum sf	Maximum sf	Expected Profit per sf
Electronics	$100	24	6,000	30,000	$12
Furniture	$50	12	10,000	30,000	$6
Men's Clothing	$30	5	2,000	5,000	$2
Clothing	$600	10	3,000	40,000	$30
Jewelry	$900	14	1,000	10,000	$20
Books	$50	2	1,000	5,000	$1
Appliances	$400	3	12,000	40,000	$13

         The company has gathered $20 million to invest in floor stock. The risk column is a measure of risk associated with investment in floor stock based on past data from other stores and accounts for outdated inventory, pilferage, breakage, and so on. For instance, electronics loses 24% of its total investment, furniture loses 12% of its total investment, and so on. The amount of risk should be no more than 10% of the total investment.

         a)     Develop a linear optimization model to maximize profit.

         b)     if the chain obtains another $1 million of investment capital for stock, what would then be the profit? Would the solution be the same?

Answer 1

a.

Below screenshot show the approach to solve this linear programming problem using Excel -> Solver.

Optimal solution as per linear model is

Department	Number of Sf
Electronics	30,000
Furniture	30,000
Men's Clothing	5,000
Clothing	12,702
Jewelry	1,000
Books	1,000
Appliances	16,946

MAX PROFIT

$1,172,375

b.

If Investment is increased from $20 m to $21m then impact on solution and profit is shown in below screenshot

Profit is now increased to

1,222,375

Optimal solution is also changed as below.

Department	Number of Sf
Electronics	30,000
Furniture	30,000
Men's Clothing	5,000
Clothing	14,369
Jewelry	1,000
Books	1,000
Appliances	16,946

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