DSC1007/DSC1007X Business Analytics 2016/17 Semester 1 NUS Business School Assignment 6 - Geometry of Linear Programming Q1. Chapter 13 Q27 (b) Q2. Chapter 13 Q43 (a) (Both Math model and Solver model) Q3. An investor is considering allocating $10,000 among five investment alternatives. The five alternatives and their respective fund categories, risk levels, and average annual returns are shown below: Name of Fund Category of Fund Risk Level Average Annual Return Adams Money Market Fund 1 4.50% Barney Money Market Fund 2 5.62% Chilton Bond Fund 2 6.80% Dunster Bond Fund 3 10.15% Excelsior Aggressive Growth Fund 5 20.60% The risk level of each investment is rated on a scale of 1 to 5, where 1 is very conservative and 5 is very risky. The investor would like to maximize the average annual return on his investment subject to the following restrictions: 1. The average risk level of the entire investment should not exceed 2.5. 2. At least 30% of the investment should be placed in money market funds. 3. At most $2,000 should be invested in the aggressive growth fund. Construct and solve a linear optimization model to determine the optimal allocation of the investor's money. Supplementary Questions (No need to submit) SQ1. A small appliance manufacturer must meet (on time) the following demands: quarter 1, 3000 units; quarter 2, 2000 units; quarter 3, 4000 units. Each quarter, up to 27000 units can be produced with regular-time labor at a cost of $40 per unit. During each quarter, an unlimited number of units can be produced with overtime labor, at a cost of $60 per unit. Of all units produced, 20% are unsuitable and cannot be used to meet demand. Also, at the end of each quarter, 10% of all units on hand spoil and cannot be used to meet any future demand. After each quarter's demand is satisfied and spoilage is accounted for, a cost of $15 per unit in ending inventor is incurred. Develop an LP model to minimize the total cost of meeting the demands of the next three quarters. Assume that 1000 usable units are available at the beginning of quarter 1