Reconsider the example illustrating the use of robust optimization that was presented in Sec. 7.4. Wyndor management now feels that the analysis described in this example was overly conservative for three reasons: (1) it is unlikely that the true value of a parameter will turn out to be quite near either end of its range of uncertainty shown in Table 7.10, (2) it is even more unlikely that the true values of all the parameters in a constraint will turn out to simultaneously lean toward the undesirable end of their ranges of uncertainty, and (3) there is a bit of latitude in each constraint to compensate for violating the constraint by a tiny bit. Therefore, Wyndor management has asked its staff (you) to solve the model again while using ranges of uncertainty that are half as wide as those shown in Table 7.10.
Answer to relevant QuestionsConsider 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 ...Consider the following constraint whose right-hand side b is assumed to have a normal distribution with a mean of 100 and some standard deviation σ. 30x1 + 20x2 ≤ b A quick investigation of the possible spread of the ...Refer to Sec. 3.4 (subsection entitled "Controlling Air Pollution") for the Nori & Leets Co. problem. After the OR team obtained an optimal solution, we mentioned that the team then conducted sensitivity analysis. We now ...Consider the following problem. Maximize Z = c1x1 + c2x2, Subject to and x1 ≥ 0, x2 ≥ 0. Let x3 and x4 denote the slack variables for the respective functional constraints. When c1 = 3, c2 = –2, b1 = 30, and b2 = ...Consider the following problem. Maximize Z = 2x1 + x2, Subject to and x1 ≥ 0, x2 ≥ 0. I (a) Solve this problem graphically. (b) Use the upper bound technique manually to solve this problem. (c) Trace graphically the path ...
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