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Running head: INDIVIDUAL PROBLEM 41Chapter 8Problem 1 Consider the following linear program:MAX3A + 2Bs.t. 1A + 1B <103A + 1B <241A + 2B <16A, B >0a.Use the graphical solution procedure to find the optimal solution. b.Assume that the objective function coefficient for a changes from 3 to 5. Does the optimal solution change? Use the graphical solution procedure to find the new optimal solution.c.Assume that the objective function coefficient for a remains 3, but the objective function coefficient for B changes from 2 to 4. Does the optimal solution change? Use the graphical solution procedure to find the new optimal solution. d.The sensitivity report for the linear program in part (a) provides the following objective coefficient range information. Variable Objective CoefficientAllowable IncreaseAllowable DecreaseA3.0003.0001.000B2.0001.0001.000Use this objective coefficient range information to answer parts (b) and (c).Problem 2Consider the linear program in Problem 1. The value of the optimal solution is 27. Suppose that the right-hand side for constraint 1 is increased from 10 to 11. a.Use the graphical solution procedure to find the new optimal solution. b.Use the solution to part (a) to determine the shadow price for constraint 1.c.The sensitivity report for the linear program in Problem 1 provides the following right- hand-side range information:
Individual Problem 42Constraint Constraint R.H. SideAllowable IncreaseAllowable Decrease110.0001.2002.000224.0006.0006.000316.000Infinite3.000What does the right-hand-side range information for constraint 1 tell you about the shadow price for constraint 1?d.The shadow price for constraint 2 is 0.5. Using this shadow price and the right-hand- side range information in part (c), what conclusion can you draw about the effect of changes to the right-hand side of constraint 2?Problem 3Consider the following linear program:Min8X + 12Y s.t.1X + 3Y >9 2X +2Y >106X + 2Y >18X,Y >0a.Use the graphical solution procedure to find the optimal solution. b.Assume that the objective function coefficient for X changes from 8 to 6. Does the optimal solution