11 To illustrate the validity of the 100% Rule for objective function coefficients, consider an LP with four decision variables (x1, x2, x3, and x4) and two constraints in which x1 and x2 are basic variables in the optimal basis. Suppose (if only a single objective function coefficient is changed) the current basis is known to be optimal for L1 c1 U1 and L2 c2 U2. Suppose we change c1 to c1 c1

c1 and c2 to c2 c2

c2, where c1 0 and c2 0. Let

Show that if r1 + r2 Hint: Any variable xj prices out to cBVB1aj cj. To show that for the new values of c1 and c2, all variables still price out nonnegative, use the fact that

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AC ' - and -Ac 12 12-12