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.

Risk as a % of $ Invested Minimum sf Maximum sf Expected Profit per sf Electronics $100 24 6,000 30,000 $12.00 Furniture $50 12 10,000 30,000 $6.00 Men’s Clothing $30 5 2,000 5,000 $2.00 Clothing $600 10 3,000 40,000 $30.00 Jewelry $900 14 1,000 10,000 $20.00 Books $50 2 1,000 5,000 $1.00 Appliances $400 3 12,000 40,000 $13.00 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is a measure of risk associated with investment in floor stock based on past data from other stores and accounts for outdated inventory, pilferage, breakage, and so on.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 the new solution be?