1. Let now be time t = 0. If we receive/pay ct t = 0, 1, 2,..., T years from now, the net present value (NPV) of this stream of cash flows is T t=0 Ct (1+r)t Where 0 < r < 1 is the discount rate. Payments are indicated when ct < 0. Suppose two investments with varying cash flows (in thousands of dollars) are available as shown in the following table. At time 0, $10,000 is available for investment, and at time 1, $7,000 is available. The discount rate is 0.10. Cash Flow in Year t Investment 0 1 2 3 1 2 -6 -5 7 9 -8 -3 9 7 (a) What is the net present value for each investment? (b) Assume that you can make a fractional investment. (That is, if you choose a 50% investment then you receive 50% of the NPV associated with that investment.) For- mulate a linear program whose solution maximizes the net present value obtained from these investments subject to the relevant constraints. (c) Graphically find an optimal solution to the LP.