New Berlin Investments is considering five investments.

New Berlin 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. New Berlin 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. New Berlin Investments can invest in at most three investments.
3. If New Berlin Investments invests in investment 3, they must also invest in investment 1.
4. If New Belin 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.