. It is late Thursday night. Your best friend is trying to finish the Math430 homework. Your friend thinks that after doing tons of calculations and many simplex iterations he/she found the optimal solution to the following LP (note the objective function is maximize):
max 8x1 −9x2 +12x3 +4x4 +11x5
s.t. 2x1 −3x2 x1 +7x2 5x1 +4x2
+4x3 +x4 +3x5 ≤1 +3x3 −2x4 +x5 ≤ 1 −6x3 +2x4 +3x5 ≤ 22
xi ≥0
Your friend claims that x ̄1 = x ̄3 = x ̄5 = 0, x ̄2 = 2 and x ̄4 = 7 is the optimal solution. Do you believe that?
By using complementary slackness, convince your friend that he/she is wrong.