Problem 1. [50 pointsl Consider the following LP max 3 2. s.t. 210 a. Use the co

Question

Problem 1. [50 pointsl Consider the following LP max 3 2. s.t. 210 a. Use the contour method to determine the optimal corner b. Apply the matrix method for sensitivity analysis to "jump" to the final optimal corner Are the values of all the variables (decision and slack) consistent with your solution in part a.? For each of the follouing subproblems, you will perform sensitivity analysis for various modifications to the LP above. For each of the subproblems, » Redraw the feasible region like in part a. For the changes, draw solid lines (contours or boundaries) for 6, = 0 and dashed lines for 6, being some number you pick. That is, you should illustrate how the problem changes geometrically. BrieHy desribe in words what changes occur ·Check that your answers with setting .-0 are consistent with part b.. ·Describe how the optimal solution is sensitive to parameter changes (eg ·0) for -the coordinates, - feasibility, optimality -and the objective value Draw sensitivity plots of the parameters for optimality (which requires feasibility). » Write "re-use work" when intermediate steps are the sane as in b.

Explanation / Answer

Solution to the given problem is obtained by moving from one corner to the other or comparing values of objective function at the basic feasible solutions (corner points) in the feasible region. Moving the objective function line as far as possible away from the origin.

The given problem with its solution is as follows:

Solution

Corner points and solution

b

Solution using simplex method

Sensitivity/ Limits/ Range report

Coefficient of X1 (objective function) may take the values from 2 to infinity

Coefficient of X2 (in objective function) may take values between zero and three.

X1 X2 RHS Equation form Maximize 3 2 Max 3X1 + 2X2 Constraint1 1 1 <= 10 X1 + X2 <= 10 Constraint 2 1 0 <= 6 X1 <= 6 Constraint3 0 1 <= 8 X2 <= 8

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