1. Consider the following LP:

Maximize z = 2xI + 3X2 subject to Xl + 3X2 :5 6 3x[ + 2x2 :5 6 1

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(a) Express the problem in equation form.

(b) Determine all the basic solutions of the problem, and classify them as feasible and infeasible.

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(c) Use direct substitution in the objective function to determine the optimum basic feasible solution.

(d) Verify graphically that the solution obtained in

(c) is the optimum LP solutionhence, conclude that the optimum solution can be determined algebraically by considering the basic feasible solutions only.

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(e) Show how the infeasible basic solutions are represented on the graphical solution space.

Determine the optimum solution for each of the following LPs by enumerating alI the basic solutions.

(a) Maximize z = 2x[ - 4X2 + 5X3 - 6X4 subject to Xl + 4X2 - 2X3 + 8X4 :5 2

-xI + 2X2 + 3X3 + 4X4 :5 1

(b) Minimize Z = XI + 2X2 - 3X3 - 2X4 subject to XI + 2X2 - 3X3 + X4 = 4 XI + 2x2 + X3 + 2x4 = 4 f

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