# Question: Consider the following problem Maximize Z c1x1 c2x2 Subject to and x1

Consider the following problem.

Maximize Z = c1x1 + c2x2,

Subject to

and

x1 ≥ 0, x2 ≥ 0.

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

(a) Use the graphical method to solve this model when using the estimates of the parameters.

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

Maximize Z = c1x1 + c2x2,

Subject to

and

x1 ≥ 0, x2 ≥ 0.

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

(a) Use the graphical method to solve this model when using the estimates of the parameters.

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

## Answer to relevant Questions

Follow the instructions of Prob. 7.4-2 when considering the following problem and the information provided about its parameters in the table below. Minimize Z = c1x1 + c2x2, subject to the constraints shown at the top of the ...Suppose that a linear programming problem has 20 functional constraints in inequality form such that their right-hand sides (the bi) are uncertain parameters, so chance constraints with some a are introduced in place of ...The Ploughman family has owned and operated a 640-acre farm for several generations. The family now needs to make a decision about the mix of livestock and crops for the coming year. By assuming that normal weather ...Consider Variation 5 of the Wyndor Glass Co. model (see Fig. 7.5 and Table 7.8), where the changes in the parameter values given in Table 7.5 are c-bar2 = 3, a-bar22 = 3, and a-bar32 = 4. Use the formula b* = S*b-bar to find ...Use the upper bound technique manually to solve the following problem. Maximize Z = x1 + 3x2 – 2x3, Subject to and x1 ≥ 0, x2 ≥ 0, x3 ≥ 0.Post your question