# Construct the coefficient matrix, define each of the variables, and explain briefly the…

Construct the coefficient matrix, define each of the variables, and explain briefly the significance of each equation or inequality in the linear-programming model for optimal operation, during March and April, of the hydroelectric power system described as follows:

The system consists of two dams and their associated reservoirs and power plants on a river. The important flows of power and water are shown in the accompanying diagram.

In the following table, all quantities measuring water are in units of 103 acre-feet (KAF). Power is measured in megawatt hours (MWH).

Power can be sold at \$5.00 per MWH for up to 50,000 MWH each month, and excess power above that figure can be sold for \$3.50 per MWH.

Assume flow rates in and out through the power plants are constant within the month. If the capacity of the reservoir is exceeded, the excess water runs down the spillway and by-passes the power plant. A consequence of these assumptions is that the maximum and minimum water-level constraints need to be satisfied only at the end of the month. (Suggestion: First set up the model for the March operating decisions, then modify it as necessary to extend the planning horizon to the end of April.

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