# Applied Mathematical Programming by Stephen P. Bradley Publication via Bradley, Stephen P., Hax, Arnoldo C., Magnanti, Thomas L.

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Extra info for Applied Mathematical Programming

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1 Simplex Method—A Preview 39 3. The righthand-side coefficients are all nonnegative. 4. One decision variable is isolated in each constraint with a +1 coefficient (x1 in constraint (1) and x2 in constraint (2)). The variable isolated in a given constraint does not appear in any other constraint, and appears with a zero coefficient in the objective function. A problem with this structure is said to be in canonical form. This formulation might appear to be quite limited and restrictive; as we will see later, however, any linear programming problem can be transformed so that it is in canonical form.

Exercises 35 24. 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).

For ≥ inequalities, let the nonnegative surplus variable represent the amount by which the lefthand side exceeds the righthand side; for ≤ inequalities, let the nonnegative slack variable represent the amount by which the righthand side exceeds the lefthand side. 3. Multiply equations with a negative righthand side coefficient by −1. 4. Add a (nonnegative) artificial variable to any equation that does not have an isolated variable readily apparent, and construct the phase I objective function. To illustrate the orderly application of these rules we provide, in Fig.