The Tatham company is considering 7 investments. The cash required for each investment and the net present value of each investment is listed below:

Investment	Investment cost	NPV
1	5000	16000
2	2500	8000
3	3500	10000
4	6000	19500
5	7000	22000
6	4500	12000
7	3000	7000

You have $15000 available to invest. Find the investment policy that maximizes your NPV. For each investment, you must either totally invest or not invest: you cannot partially invest in a project.

Questions:

Complete model with the optimal solution in Excel tab

What is the optimal investment strategy, and what is the total NPV?

Assume that you add the constraint that if you invest in investment 5 (auto assembly) you must also invest in investment 7 (tire manufacturing), but not the other way around. What constraint would you add? What is the new optimal investment strategy and NPV?

Go back to your original model (without the auto constraint). Assume that you can invest in investment 1 or investment 2 or neither, but not both. They are both related to the economy in a single developing nation, and you want to limit your risk by not investing in 2 projects there. What is the constraint in algebraic form? What is the new optimal policy and resulting NPV?

Fractional portion (also known as the LP Relaxation)

Solve the fractional form of the problem (the LP Relaxation), assuming you can invest in partial investments. Whats the optimal strategy? (assume there are not additional constraints on investments 1&2: go back to your original model). What is the NPV?

Also run the sensitivity report. What is the value (the shadow price) associated with increasing your budget?

Calculate the NPV/investment dollar for each investment. What can you say about how the fractional solution chose investments? Does the shadow price you just calculated match one of these ratios? Which one? Explain why.