Just Sports $27.50 Sports 'N Stuff $40.00 $30.00 The Sports Dude Sports of All Sorts needs to forecast the demand at each of its four retail locations file for next year, and then plan how to produce and distribute its product from the fac- ards cities through the DCs to the retailers. The file Skateboards contains five tabs: Plant Capacities, Transportation Costs, DC Capacities, DC Processing Co ing Costs, and Historical sumes Demand. ncepts " Construct a scatter plot for the historical demand for each retailer. Use the historical pter 8. demand to forecast the future demand for each retailer. For Just Sports and Sports 'N Stuff, use the average of the historical demands as the forecast for the next year. For The Sports Dude, use simple linear regression to forecast the demand for the next year. Round your forecast to the nearest one thousand units (e.g., if your forecast is 12,303, round to 12,000 for use in part (b). b. Construct a linear programming model of the supply chain. c. Solve the linear programming model you constructed in part (b). What is the total cost? Which plants are planned to use all of their capacity? Which distribution cen- ters will use all of their capacity? CASE PROBLEM: INVESTMENT STRATEGY . . . . . . . . . . . . J. D. Williams, Inc. is an investment advisory firm that manages more than $120 million in funds for its numerous clients. The company uses an asset allocation model that rec- ommends the portion of each client's portfolio to be invested in a growth stock fund, an income fund, and a money market fund. To maintain diversity in each client's portfolio, the firm places limits on the percentage of each portfolio that may be invested in each of the three funds. General guidelines indicate that the amount invested in the growth fund must be between 20% and 40% of the total portfolio value. Similar percentages for the other two funds stipulate that between 20% and 50% of the total portfolio value must be in the income fund and that at least 30% of the total portfolio value must be in the money market fund. In addition, the company attempts to assess the risk tolerance of each client and adjust the portfolio to meet the needs of the individual investor. For example, Williams just con- tracted with a new client who has $800,000 to invest. Based on an evaluation of the client's risk tolerance, Williams assigned a maximum risk index of 0.05 for the client. The firm's risk indicators show the risk of the growth fund at 0.10, the income fund at 0.07, and the money market fund at 0.01. An overall portfolio risk index is computed as a weighted aver- age of the risk rating for the three funds, where the weights are the fraction of the client's portfolio invested in each of the funds. Additionally, Williams is currently forecasting annual yields of 18% for the growth fund, 12.5% for the income fund, and 7.5% for the money market fund. Based on the infor- mation provided, how should the new client be advised to allocate the $800,000 among the growth, income, and money market funds? Develop a linear programming model that