Consider the following problem. Maximize Z = 2 x 1 x 2 + x 3 ,
Question:
Consider the following problem.
Maximize Z = 2x1 − x2 + x3,
subject to
and
x1 ≥ 0, x2 ≥ 0, x3 ≥ 0.
If we let x4, x5, and x6 be the slack variables for the respective constraints, the simplex method yields the following final set of equations:
Now you are to conduct sensitivity analysis by independently investigating each of the following eight changes in the original model. For each change, use the sensitivity analysis procedure to revise this set of equations (in tableau form) and convert it to proper form from Gaussian elimination for identifying and evaluating the current basic solution. Then test this solution for feasibility and for optimality. If either test fails, reoptimize to find a new optimal solution.
(a) Change the right-hand sides to
(b) Change the coefficient of x3 in the objective function to c3 = 2.
(c) Change the coefficient of x1 in the objective function to c1 = 3.
(d) Change the coefficients of x3 to
(e) Change the coefficients of x1 and x2 to
respectively.
(f) Change the objective function to Z = 5x1 + x2 + 3x3.
(g) Change constraint 1 to 2x1 − x2 + 4x3 ≤ 12.
(h) Introduce a new constraint 2x1 + x2 + 3x3 ≤ 60.
Expert Answer:
