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**Unformatted text preview: **PROBLEMS .' ~,. ti: ~ ff 1. Recall the RMC problem (Chapter 2, Problem 21). Letting F = tons of fuel additive S = tons of solvent base leads to the formulation Max 40F + 30S s.t. %F + %S:$ 20 ¥SS :$ 5 %F + %oS :S 21 , ~S~O Use the graphical sensitivity analysis approach to determine the range of optimality for the ~ . ' objectivefunctioncoefficients. ,I 2. For Problem 1 use the graphical sensitivity approach to determine what happens if an ad- ditional3 tons of material 3 tIec,?me available. What is the corresponding dual price for the oons~a ~ 3. Considerthe followinglinear program: Material 1 Material 2 Material 3 s.t. XI + X2:S 10 2x1 + X2 ~ 4 XI + 3X2 :S 24 2x1 + X2:$ 16 XI' X2.~ a. Solve this problem using the graphical solution procedure. b. Compute therangeofoptimality fortheobjectivefunctioncoefficientof XI' ' c. Computethe range of optimalityfor the objectivefunctioncoefficientof X2' '1 d. Suppos~ the obj~ve function coefficient of XI is increased from 2 to 2.5. What is the . new Optimalsolution? e. Suppose the objective function coefficient of X2 is decreased from 3 to 1. What is the 1 newoptimalsolution'? .~ 4. Refer to Problem3. Computethe dual pricesfor co~ts 1 and 2 and interpretthem. ,~ :5. ,Consider the following linear program: ' Min s.t. XI + 2x2 ~ 7 2x1 + x2 ~ 5 xI + 6x2 ~ 11 xI,X2 ~ a. Solve this problem using the graphical solution procedure. b. Compute the range of optimality for the objective function ooefficient of XI. 'c. Compute the range of optimality for the objective function coefficient of X2' d. Suppose the objective function coefficient of xI is increased to 1.5. Find the new op- timal solution. e. Supposethe objectivefunctioncoefficientof X2 is decreasedto VS.Find the new opti- mal solution. PDF processed with CutePDF evaluation edition www.CutePDF.com Chapter 3 Linear Programming: Sensitivity Analysis and Interpretation of Solution 131 6. Refer to Problem 5. Compute and interpret the dual prices for the constraints. 7. Consider the following linear program: Max s.t. 2xI + X2 ~ 3 I- XI + 5X2 ~ 4 1- 2xI- 3X2 :S 6 ; 3Xl + 2X2 :S 35 if- %Xl + X2:S 10 =S Xl,X2 ~ a. Solve this problem using the graphical solution procedure. b. Compute the range of optimality for the objective function coefficient of XI' c. Compute the range of optimality for the objective function coefficient of X2' d. Suppose the objective function coefficient of Xl is decreased to 2. What is the new op- timal solution? e. Suppose the objective function coefficient of X2 is increased to 10. What is the new optimal solution? 8. Refer to Problem 7. Suppose that the objective function coefficient of X2 is reduced to 3. a. Re-solve using the graphical solution procedure....

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