Question: Consider the following LP: (a) Convert the LP given above to the standard form in which the necessary slack, excess and artificial variables are added.

Consider the following LP:

Maximize z= 2x, +4x2 +3x3z+3x4 Subject to X, + X, + X3

(a) Convert the LP given above to the standard form in which the necessary slack, excess and artificial variables are added.

(b) Convert the LP given above to the canonical form (Hint: Do not use any slack, excess, and artificial variables).

(c) Using the relevant formulas, determine the tableau to the LP model where x1 and x2 are the basic variables. Is the solution optimal? If not, start with this solution and find the optimal solution.

(d) Write the dual of the problem.

Maximize z= 2x, +4x2 +3x3z+3x4 Subject to X, + X, + X3 = 4 X, +4x2 - 4x4 =8 X1, X2 , X3 2 0, x4 50

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