# Question: Consider the following problem Maximize Z 5x1 c2x2

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.

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