Question: Consider the following parametric linear programming problem. Maximize Z() 2x1 4x2 5x3, subject to x1 3x2 2x3 5 x1

Consider the following parametric linear programming problem.

Maximize Z() 2x1 4x2 5x3, subject to x1 3x2 2x3 5

x1 2x2 3x3 6 2

and x1 0, x2 0, x3 0, where can be assigned any positive or negative values. Let x4 and x5 be the slack variables for the respective functional constraints.

After we apply the simplex method with 0, the final simplex tableau is

(a) Express the BF solution (and Z) given in this tableau as a function of . Determine the lower and upper bounds on before this optimal solution would become infeasible. Then determine the best choice of between these bounds.

(b) Given that is between the bounds found in part (a), determine the allowable range to stay optimal for c1 (the coefficient of x1 in the objective function).

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