1. Consider the following linear programming problem:
minimize Z = 1.01x1-x2
subject to -x1 + x2 ≥ 0
−x1 −x2 ≥−3
with x1,2 ≥ 0
(a) Write the problem in standard form.
(b) Solve the problem in standard form graphically. Also,
• Introduce appropriate slack or surplus variables and define the boundaries of the feasible region in your graphical representation.
• Explain why slack variables are added and not subtracted from the left hand sides of the constraints.
• Indicate the shortest path to optimality.
(c) Solve the problem manually using the simplex algorithm. Determine the optimal solution
x* and the optimal value Z*. Explain every step you make. In particular
• How do you choose certain values to enter the basis? Explain why.
• How do you choose which variables should leave the basis? Explain why.
• How do you decide when to stop? Explain why.
"a)
from graphical solution,
z(0, 0) = 0
z (3, 3) = 3.03-3 = 0.03
z(0, 3) = 1.01*0 - 3 = -3"
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