Jaycee's department store chain is planning to open a new store. It needs to decide how to allocate the100,000 square feet of available floor space among seven departments. The accompanying data includes the expected performance of each department permonth, in terms of square feet(sf). 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 outdatedinventory, pilferage,breakage, and so on. Forinstance, electronics loses24% of its totalinvestment, furniture loses12% of its totalinvestment, and so on. The amount of risk should be no more than10% of the total investment. Assume that it is not required that the entire available floor space be used. Answer parts a and b below.

Department Investment/sf Risk as a % of $ invested Minimum sf Maximum sf Expected Profit per sf

Electronics 100 24 6000 30000 13.00

Furniture 50 12 12000 30000 6.00

Men's Clothing 30 5 2000 5000 2.00

Clothing 600 10 2000 40000 30.00

Jewelry 900 14 1000 10000 21.00

Books 50 2 1000 5000 2.00

Appliances 400 3 13000 41000 14.00

a. Develop a linear optimization model to maximize profit. Complete the table below to indicate the number of square feet perdepartment, and then give the total profit.