Many investments and capital budgeting models involve 0-1 binary variables and integer programming. Consider Marquette Investments, a venture capital firm that is evaluating six different investment opportunities. There is not sufficient capital to invest in all of them, but more than one is likely to be selected.

Investment 1 will yield a net present value (NPV) of $765,000, investment 2, an NPV of $830,000, investment 3, an NPV of $235,000, investment 4, an NPV of $512,000, investment 5 an NPV of $308,000 and investment 6 an NPV $550,000. 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, $200,000, investment 2, $220,000, investment 3, $100,000, investment 4, $155,000, investment 5, $120,000 and investment 6 $145,000. At present $700,000 is available for investment.
2. Marquette Investments should invest in at least 3 of these investments.
3. Either investment 1 or 4 must be selected, but not both.
4. If investment 4 is selected, then investment 6 must also be selected.
5. Investment 5 can only be selected if investment 1 is selected and not investment 3.

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 1-6.

Y_i = 1 if investment I is made, 0 otherwise, (i = 1,2,3,4,5, 6).

1. Write down the objective function.

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

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

4. Write down the constraint corresponding to policy (iii)

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

6. Write down the constraint corresponding to policy (v)

7. Integrality constraint (already done)

Y_i = 0 or 1 (I = 1,2,3,4,5,6)