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Imagine that you work as a financial advisor. You have a client who would like to invest $750,000 in bonds. You have narrowed down your options to the following list:

Company Interest Rate. years to Maturity, Rating

Acme Chemical 8.65%, 9, 1 - Excellent

DynaStar 9.40%, 10, 3 - Good

Eagle Vision 10.00%, 6, 4 - Fair

Micromodeling 8.85%, 10, 1 - Excellent

OptiPro 9.15%, 7, 3 - Good

Sabre Systems 9.1%, 13, 2 - Very Good

The interest rate describes the return of the investment as the simple interest earned over the length of the bonds life. That is, if $100 is invested in Acme Chemical, the return at the end of the 9 years will be P V r = 100 0.0865 = $8.65.

1. No more than 25% of the total funds should be invested in any one investment.

2. At least half should be invested in long-term bonds that mature in ten years or more.

3. No more than 35% of the total funds should be invested in the combination of DynaStar, Eagle Vision, and Optipro. And the last stipulation is that all $750,000 must be invested. If the goal is to maximize your clients total return on the investment, how much should they invest in each of the six bonds? What is the corresponding maximum total return they can expect to receive?

1. (3 points) Define the variables of the problem (dont forget to include a unit/quantifier for each!).

2. (2 points) Define the objective function. 1

3. (6 points) Define the constraints (hint: this should include six non-negativity constraints).

4. (4 points) State the problem mathematically as a linear programming problem (use the standard form we typically state LP problems in). 2

5. (6 points) Fill out the Excel sheet and use it to set up Solver. After running Solver and obtaining the solution, upload your Excel sheet to the dropbox on D2L.

6. (3 points) State the optimal solution and corresponding optimal value of the objective function found by Solver.

7. (4 points) Use your solution to answer the original question: how much should they invest in each of the six bonds? What is the corresponding maximum total return they can expect to receive?

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