Consider the following linear programming problem
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Consider the following linear programming problem

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.

Hint

Mathematics

"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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