Consider the following LP and the corresponding optimal tableau:

Problem #2

1. Using sensitivity analysis, nd the optimal solution of the above LP if the coecient of x2 in the objective function is changed from 1 to 5.

2. Suppose that the coecient of x2 in the rst constraint is changed from 2 to 1/6. Using sensitivity analysis, nd the optimal solution of the above LP.

3. Suppose that the following constraint is added to the problem:

x2 + 2x3 = 3

Using sensitivity analysis, nd the optimal solution of the above LP.

4. If you were to choose between increasing the right-hand-side of the rst and second constraints by 1 unit, which one would be benecial for the objective function value? Why? What is the eect of this increase on the optimal value of the objective function?

5. Suppose that a new activity x6 is proposed with unit return (objective function coecient) 6 and consumption vector (coecient vector) a6 = [2, 1]T . Find the optimal solution of the above LP using the sensitivity analysis.

Consider the following LP and the corresponding optimal tableau: Maximizesubjectto2x1+x2x3x1+2x2+x38x1+x22x34x1,x2,x30. 1. Using sensitivity analysis, find the optimal solution of the above LP if the coefficient of x2 in the objective function is changed from 1 to 5 . 2. Suppose that the coefficient of x2 in the first constraint is changed from 2 to 1/6. Using sensitivity analysis, find the optimal solution of the above LP. 3. Suppose that the following constraint is added to the problem: x2+2x3=3 Using sensitivity analysis, find the optimal solution of the above LP. 4. If you were to choose between increasing the right-hand-side of the first and second constraints by 1 unit, which one would be beneficial for the objective function value? Why? What is the effect of this increase on the optimal value of the objective function? 5. Suppose that a new activity x6 is proposed with unit return (objective function coefficient) 6 and consumption vector (coefficient vector) a6=[2,1]T. Find the optimal solution of the above LP using the sensitivity analysis