Question: Consider the following linear programming problem. Max 5x1 6x2 4x3 s:t: 3x1 4x2 2x3 120 x1 2x2 x3

Consider the following linear programming problem. Max 5x1 þ 6x2 þ 4x3 s:t: 3x1 þ 4x2 þ 2x3 120 x1 þ 2x2 þ x3 50 x1 þ 2x2 þ 3x3 30 x1; x2; x3 0 The optimal simplex tableau is: x1 x2 x3 s1 s2 s3 Basis cB 5 6 4 0 00 s3 00 4 0 2 71 80 x3 40 2 1 1 30 30 x1 5 1 0 01 2 0 20 zj 5 8 4 1 20 220 cj – zj 0 2 0 1 2 0

a. Calculate the range of optimality for c1.

b. Calculate the range of optimality for c2.

c. Calculate the range of optimality for cs1 .

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