13. Consider the problem Maximize z "" XI + X2 subject to 2Xl + X2 :$ 6 XI + 2X2 :::;; 6 Xl + X2 ~ 0

(a) Show that the optimal basic solution includes both Xl and X2 and that the feasibility ranges for the two constraints, considered one at a time, are - 3 ~ DI :OS 6 and

-3 :::;; D2 :::;; 6.

*

(b) Suppose that the two resources are increased simultaneously by 6. > 0 each. First, show that the basic solution remains feasible for all 6. > O. Next, show that the 100% rule will confirm feasibility only if the increase is in the range 0 < A :$ 3 units. Otherwise, the rule fails for 3 < Ii ~ 6 and does not apply for 6. > 6.