Consider the two versions of the dual problem for the radiation therapy example that are given in Tables 6.15 and 6.16. Review in Sec. 6.4 the general discussion of why these two versions are completely equivalent. Then fill in the details to verify this equivalency by proceeding step by step to convert the version in Table 6.15 to equivalent forms until the version in Table 6.16 is obtained.
Answer to relevant QuestionsFor each of the following linear programming models, give your recommendation on which is the more efficient way (probably) to obtain an optimal solution: by applying the simplex method directly to this primal problem or by ...Consider the following problem. Minimize Z = –x1 – 3x2, Subject to and x1 ≥ 0, x2 ≥ 0. (a) Demonstrate graphically that this problem has an unbounded objective function. (b) Construct the dual problem. Consider the following problem. Maximize Z = 3x1 + x2 +4x3, Subject to and x1 ≥ 0, x2 ≥ 0, x3 ≥ 0. Reconsider the model of Prob. 7.2-2. Suppose that the right-hand sides of the functional constraints are changed to 20 + 2θ (for constraints 1) and 90 – θ (for constraint 2), where θ can be assigned any positive or ...David, LaDeana, and Lydia are the sole partners and workers in a company which produces fine clocks. David and LaDeana each are available to work a maximum of 40 hours per week at the company, while Lydia is available to ...
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