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Solutions Manual for Deterministic Operations Research Models and Methods in Linear Optimization, 1e David J. Rader (All Chapters) 1 / 4
Chapter 1 1.1. (a) The optimal solution occurs at (0,10) with optimal value 20.(b) The optimal solution occurs on the line segment joining (3,6) and (6,3) with optimal value 9.
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4CHAPTER 1.
(c) The optimal solutions on the line segment joining occursat (0,150) and (100,100) with optimal value 7500.(d) The optimal solution occurs at (2,1) with optimal value 7.(e) The feasible region is empty, and hence there is no optimal solution.
1.2. (a) The optimal range for coefficientcxofxiscx≤4. The range for coefficientcyofyiscy>= 1.5.(b) For optimal solution (6,3) to remain optimal, the coefficientcxofxmust be so that the slope of the objective line remains negatives, which indicates that−cx≤ −1 or thatcx≥1, while the coefficientcyofymust be in the interval−2≤cy≤1. For the optimal solution (3,6) to remain optimal, the coefficientcxmust remain in the interval−2≤cx≤1 while the coefficientcyofy must satisfycy≥1, since it must remain positive and the slope of the objective line must be no more than−1. 3 / 4
5 (c) For the solution (0,150) to remain optimal, the coefficientc1ofx1must satisfyc1≥25, and the coefficientc2must satisfyc2≥50. For the solution (100,100) to remain optimal, we must have 25≤c1≤50 and 25≤c2≤50.(d) For (2,1) to remain optimal the coefficientc1ofx1must satisfy−3≤c1≤ 3 2 and the coefficient c2ofx2must satisfyc2≥2.(e) The feasible region is empty, and hence there is no optimal solution.
1.3. The optimal solution occurs at (4,0) with optimal value 68.
1.4. The optimal solution occurs at (2,1) with optimal value 8.
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