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 below.

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is a measure of risk associated with investment in floor stock based on past data from other stores and accounts for outdated inventory, pilferage, breakage, etc. For instance, electronics loses 24% of its total investment, furniture loses 12% of its total investment, etc.

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?

Risk as a % of $ Department Investmen/sfinvested $100 50 30 600 900 50 400 24% 12% 5% 10% 1490 2% 3% mum sf maximum sfexpected profitsf 6000 10000 2000 3000 1000 1000 12000 $12 Electronics Furniture Men's Clothing Clothing Jewelry Books Appliances 30000 30000 5000 40000 1000 5000 40000 6.00 2.00 30.00 20.00 1.00 13.00