13 In this problem, we sketch a proof of the 100% Rule for right-hand sides. Consider an LP with two constraints and right-hand sides b1 and b2. Suppose that if only one right-hand side is changed, the current basis remains optimal for L1 b1 U1 and L2 b2 U2. Suppose we change the right-hand sides to b1 b1

b1 and b2 = b2 +b2,

Transcribed Image Text:

where Ab, > 0 and Ab < 0. Let = Ab U - b -Ab and 12 = b- L2 Show that if r + r = 1, the current basis remains optimal. (Hint: You must show that