1. Write the mathematical model. (15 marks)

2. Solve it using Excel solver. (15 marks)

A construction company is considering a number of different development projects. The cash outflows that would be required to complete each project are indicated in the table below, along with the expected net present value of each project and available new money is each year (all values in millions of dollars). Year Project 3 1 2 4 5 1 8 10 4 14 12 6 Available new money 42 25 16 12 2 6 9 3 6 3 3 7 4 6 2 0 5 7 0 4 NPV 5 15 12 20 9 21 Each project must be done in full (with the corresponding cash flows for all four years) or not done at all. Furthermore, there are the following additional considerations: Project 1 cannot be done unless Project 2 is also undertaken, and projects 3 and 4 would compete with each other, so they should not both be chosen. Any available money not spent in a given year is then available to spend in the following year. They want to choose their projects so as to maximize their total expected NPV