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.

- 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.
- New Berlin Investments can invest in at most three investments.
- If New Berlin Investments invests in investment 3, they must also invest in investment 1.
- If New Belin Investments invests in investment 3, they cannot invest in investment 4.
- If investments 1 and 2 are chosen, then investment 5 must be chosen.