Question

9. Solve the below problem using DP. Define the stage and state variables. A water resources agency has three projects in which it can invest. According to the level of investment in each project, a benefit is achieved as in the following table Investment ( million) Total Bendit Smilion) Net Benet (mille) Project The agency wants to maximize net benefits.

Answer 1

A water resource agency has 3 projects in which it can invest. The above table summarises the investment and corresponding Total and Net benefits.

When the agency can invest $5 mn, it can invest in Project 2 which gives the maximum Net benefit of $7 mn among the investments in other projects.

When the agency can invest $10 mn, it can invest 5mn in Project 2 and 5mn in Project 3 which gives the maximum Net benefit of $10 mn among the investments in other projects.

When the agency can invest $15 mn, it can invest 5mn in Project 2 and 10mn in Project 3 which gives the maximum Net benefit of $13 mn among the investments in other projects.

When the agency can invest $20 mn, it can invest 5mn in Project 2 and 15mn in Project 3 which gives the maximum Net benefit of $16 mn among the investments in other projects.

When the agency can invest $25 mn, it can invest 5mn in Project 2 and 15mn in Project 3 which gives the maximum Net benefit of $16 mn among the investments in other projects.