Part 2: Linear Programming

Suppose that you are considering investing some of your money ($10,000) into two assets: government bonds and the stock market. You anticipate that the return rate for government bond is 10% and for the stock market is 20%. Since the stock market is riskier, you do not want to put more than $4,000 in it. Similarly, you plan to spend at least $3,000 on the government bonds.

What will be your investment portfolio in order to maximize your total return? (Assume all for one year investment.)

1. Formulate the business scenario as a linear programming problem. Show the objective, the constraints, and decision variables.
2. Use the graphic approach (in Word/Excel or hand drawing) to show the constraints, the feasible region, and the optimal solution.
3. Use Excel OM package or Excel Solver Add-in to help you solve the problem. What are the optimal decisions and what is the optimal objective value?
4. Recently, there is a promotion for savings with 5% interest rate, and you would like to keep exact $1,000 savings in your total investment. Formulate these changes as a new LP problem to show the objective, the constraints, and decision variables.
5. Use Excel OM package or Excel Solver Add-in to help you solve the new LP problem above. What are the optimal decisions and what is the optimal objective value?