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.

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is a measure of risk associated with investment in floor stock based on past data from other stores and accounts for outdated in-ventory, pilferage, breakage, and so on.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 Chapter 14 Applications of Linear Optimization 501 8. The Children’s Theater Company is a nonprofit corporation managed by Shannon Board. The theater performs in two venues: Kristin Marie Hall and the Lauren Elizabeth Theater. For the upcoming season, seven shows have been chosen. The question Shannon faces is how many performances of each of the seven shows should be scheduled. A financial analysis has estimated revenues for each performance of the seven shows, and Shannon has set the minimum number of performances of each show based on union agreements with Actor’s Equity Association and the popularity of the shows in other markets. These data are shown in the table at the right. Kristin Marie Hall is available for 60 performances during the season, whereas Lauren Elizabeth Theater is available for 150 performances. Shows 3 and 7 must be performed in Kristin Marie Hall, and the other shows are performed in either venue. The company wants to achieve revenues of at least $ 550,000 while minimizing its production costs. Develop and solve a linear optimization model to determine the best way to schedule the shows. Is it possible to achieve revenues of $ 600,000? What is the highest amount of revenue that can be achieved? Show Revenue Cost Minimum Number of Performances 1 $ 2,217 $ 968 32 2 $ 2,330 $ 1,568 13 3 $ 1,993 $ 755 23 4 $ 3,364 $ 1,148 34 5 $ 2,868 $ 1,180 35 6 $ 3,851 $ 1,541 16 7 $ 1,836 $ 1,359 21 Department Investment/ sf 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?

Department Electronics Furniture Men's Clothing Clothing Jewelry Books Appliances Investment/st $100 $50 $30 $600 $900 $50 $400 Risk as a % of Invested 24 12 5 10 14 2 3 Minimum st 6,000 10,000 2,000 3,000 1,000 1,000 12,000 Maximum st 30,000 30,000 5,000 40,000 10,000 5,000 40,000 Expected Profit per sf $12.00 $6.00 $2.00 $30.00 $20.00 $1.00 $13.00