In Chapter 2 we wrote a system of linear equations using matrix notation. Similarly, we can use matrix notation to write a system of linear inequalities.
- (a) Find matrices A, B, C, and X such that the maximization problem in Example 1 of Section 4.1 can be written as
(Hint: Let B and X be column matrices, and C a row matrix.)
- (b) Show that the dual of the problem in part (a) can be written as
where Y is a row matrix.
- (c) Show that for any feasible solutions X and Y to the original and dual problems, respectively, CX ≤ YB. (Hint: Multiply both sides of AX ≤ B by Y on the left. Then substitute for YA.)
EXAMPLE 1 Slack Variables
Restate the following linear programming problem by introducing slack variables.
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EBK FINITE MATHEMATICS AND CALCULUS WIT
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