# Question

Consider the following problem.

Maximize Z = 5x1 + c2x2 + c3x3,

Subject to

and

x1 ≥ 0, x2 ≥ 0, x3 ≥ 0.

The estimates and ranges of uncertainty for the uncertain parameters are shown in the next table.

(a) Solve this model when using the estimates of the parameters.

(b) Now use robust optimization to formulate a conservative version of this model. Solve this model. Show the values of Z obtained in parts (a) and (b) and then calculate the percentage decrease in Z by replacing the original model by the robust optimization model.

Maximize Z = 5x1 + c2x2 + c3x3,

Subject to

and

x1 ≥ 0, x2 ≥ 0, x3 ≥ 0.

The estimates and ranges of uncertainty for the uncertain parameters are shown in the next table.

(a) Solve this model when using the estimates of the parameters.

(b) Now use robust optimization to formulate a conservative version of this model. Solve this model. Show the values of Z obtained in parts (a) and (b) and then calculate the percentage decrease in Z by replacing the original model by the robust optimization model.

## Answer to relevant Questions

Consider the following problem. Minimize W = 5y1 + 4y2, Subject to and y1 ≥ 0, y2 ≥ 0. Because this primal problem has more functional constraints than variables, suppose that the simplex method has been applied directly ...Reconsider the example illustrating the use of stochastic programming with recourse that was presented in Sec. 7.6. Wyndor management now has obtained additional information about the rumor that a competitor is planning to ...This case is a continuation of Case 4.3, which involved the Springfield School Board assigning students from six residential areas to the city’s three remaining middle schools. After solving a linear programming model for ...Consider the following problem. Maximize Z = x1 – x2, Subject to and x1 ≥ 0, x2 ≥ 0, (a) Solve this problem graphically. (b) Use the dual simplex method manually to solve this problem. (c) Trace graphically the path ...Use the upper bound technique manually to solve the following problem. Maximize Z = 2x1 + 5x2 +3x3 + 4x4 + x5, Subject to and 0 ≤ xj ≤ 1, for j = 1, 2, 3, 4, 5Post your question

0