Marquette Investments is considering five investments. Investment 1 will yield a net present value (NPV) of $15,000; investment 2, an NPV of $20,000; investment 3, an NPV of $15,000; investment 4, an NPV of $8,000, and investment 5, an NPV of $6,000. Marquette Investments wants to maximize its NPV obtained from investments, subject to the following constraints.

1. Each investment requires a certain cash outflow at the present time: investment 1, $6,000; investment 2, $7,000; investment 3, $3,000; investment 4, $3,000, and investment 5, $2,000. At present $14,000 is available for investment.
2. Marquette Investments can invest in at most three investments.
3. If Marquette Investments invests in investment 3, they must also invest in investment 1.
4. If Marquette Investments invests in investment 3, they cannot invest in investment 4.
5. If investments 1 and 2 are chosen, then investment 5 must be chosen.

Using ONLY the following decision variables (no need to define any more decision variables), formulate an integer program whose solution will tell Marquette Investments how to maximize the NPV obtained from investments 1-5.

a)Write down the objective function.

b)Write down the constraint corresponding to policy (i).

c)Write down the constraint corresponding to policy (ii).

d)Write down the constraint corresponding to policy (iii)

e)Write down constraint corresponding to policy (iv).

f)Write down the constraint corresponding to policy (v)

g)Integrality constraint (already done).