Question: 4. Reconsider the model in Problem 3 with objective function Maximize Z=c1x1+c2x2, where c10,c20. Use the sensitivity analysis on the objective coefficients to answer the

4. Reconsider the model in Problem 3 with

4. Reconsider the model in Problem 3 with objective function Maximize Z=c1x1+c2x2, where c10,c20. Use the sensitivity analysis on the objective coefficients to answer the following questions. (a) Find the range of c2c1, such that the optimal solution remains as (x1,x2)=(3,4). (b) Find the range of c2c1, such that the optimal solution remains as (x1,x2)=(4,2). (c) Find the range of c2c1, such that the optimal solution remains as (x1,x2)=(0,5). (d) If c1 and c2 are allowed to be negative, find the conditions on c1 and c2, and the range of c2c1 such that the optimal solution remains as (x1,x2)=(4,0). Question 3 is given as follows: 3. Consider the following problem. MaximizeZ=3x1+2x2, subject to x14 (resource 1) x1+3x215 (resource 2) 2x1+x210 (resource 3) and x10,x20,x30. The optimal solution is (x1,x2)=(3,4) with Z=17. (a) Is any of these three constraints binding constraint? (b) Use graphical analysis to determine the shadow prices for the respective resources. 4. Reconsider the model in Problem 3 with objective function Maximize Z=c1x1+c2x2, where c10,c20. Use the sensitivity analysis on the objective coefficients to answer the following questions. (a) Find the range of c2c1, such that the optimal solution remains as (x1,x2)=(3,4). (b) Find the range of c2c1, such that the optimal solution remains as (x1,x2)=(4,2). (c) Find the range of c2c1, such that the optimal solution remains as (x1,x2)=(0,5). (d) If c1 and c2 are allowed to be negative, find the conditions on c1 and c2, and the range of c2c1 such that the optimal solution remains as (x1,x2)=(4,0). Question 3 is given as follows: 3. Consider the following problem. MaximizeZ=3x1+2x2, subject to x14 (resource 1) x1+3x215 (resource 2) 2x1+x210 (resource 3) and x10,x20,x30. The optimal solution is (x1,x2)=(3,4) with Z=17. (a) Is any of these three constraints binding constraint? (b) Use graphical analysis to determine the shadow prices for the respective resources

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