Consider the problem Maximize z = x1 + x2 subject to 2x1 + x2 … 6 x1 + 2x2 … 6 x1 + x2 Ú 0

(a) Show that the optimal basic solution includes both x1 and x2 and that the feasibility ranges for the two constraints, considered one at a time, are -3 … D1 … 6 and

-3 … D2 … 6.

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(b) Suppose that the two resources are increased simultaneously by  7 0 each. First, show that the basic solution remains feasible for all  7 0. Next, show that the 100% rule will confirm feasibility only if the increase is in the range 0 6  … 3 units.

Otherwise, the rule fails for 3 6  … 6 and does not apply for  7 6.