The following problem is adapted from Sathaye and Hall (1976). A long aqueduct is to be sized by…

The following problem is adapted from Sathaye and Hall (1976). A long aqueduct is to be sized by sections to deliver irrigation water to n irrigation districts, as shown in the sketch below. The amount of water to be used by each district is to be determined.

The following problem is adapted from Sathaye and Hall (1976). A long aqueduct is to be sized by...

It is desired to maximize overall net benefits of the project.

(a) Write the mathematical programming model for the problem.

(b) Write the dynamic programming recursive equation that will solve the problem.

(c) If 1,100,000 acre-feet of water were available (equal to Q), and were broken into 100,000 AF increments, and districts: (1) How many possible solutions are there (by enumeration)? (2) How many allocations will have to be compared using DP?

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