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.

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2 2 ax a221 Parameter a11 a12 a21 2z bi Estimate Range of Uncertainty 0.9 1.1 1.6 2.4 1.8 2.2 0.8 1.2 8.5 -9.5 7.6-8.4 2.7-3.3 3.6-4.4 b2 C1 C2