2- Consider the Rise Bakery problem in your chapter 3 part homework. Use the fol
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Question
2- Consider the Rise Bakery problem in your chapter 3 part homework. Use the following sensitivity report for this LP model to answer the following questions.
a. How much does the profit change if the bakery increases the bride dream cake price by $2? b. Changing the baking plan is very difficult for the bakery. What is the highest price that the bakery can ask for the blueberry cake to increase their total profit with the same baking plan (number of cakes)? How much does the new price increase the total profit? c. Suppose that the criteria on baking at least 5 Bride dream cake is eliminated. How much and in which direction does it change the objective function? Does it change the optimal decision variables value as well? If yes, in which direction? d. Based on some emergency condition for the operator of mixing station, he is available just for 39 hours in the following week. On the other hand, the operator of the final design station announced that he is available for 46 hours in the following week. How do these changes affect the objective function in the same week? Does that change the1 optimal decision variables value as well?
Original Problem - - -
Variable Cells Cell SBS4 Number of cakes Blueber SCS4 Number of cakes Go Spurs SDS4 Number of cakes Bride dream Final Reduced ObjectiveAllowable Allowable Value Cost Coefficient Increase Decrease 8.2 11.1 6.85 Name 41.5 27.5 1.05 0.271428571 0.38 7.84 1.26 1E+30 Constraints Final Shadow Constraint Allowable Allowable Value Price R.H. Side Increase Decrease Cell SE$16 Blueberry minimum SES17 Go Spurs minimum SE$18 Bride dream minimum SES9 Mixin SES10 Bakin SES11 Final design SES12 Packing SE$13 Blueberry maximum SE$14 Go Spurs maximum SE$15 Bride dream maximum Name 41.5 27.5 36.5 22.5 5 1.976744186 40 0.607142857 1E+30 1E+30 1E+30 5 2.25 3.5 2.25 0.708333333 7.84 3.8 40 76.5 45 7.4 41.5 27.5 80 45 12.6 50 50 50 1E+30 1E+30 1E+30 1E+30 8.5 22.5 45Explanation / Answer
a. Refer sensitivity report, allowable increase for coefficient of Bride dream cake is 7.84, which is more than $ 2. Therefore, if the price of Bride dream cake is increased by $ 2, then the optimal solution remains unchanged, because it is still within the optimality range.
b. Allowable increase for Blueberry cake is 1.05. Therefore, the bakery can increase Blueberry cake price by $ 1.05 without changing the baking plan.
New price increases the total profit by = 41.5*1.05 = $ 43.58
c. Shadow price of this constraint is -7.84, which means elminating this restriction (decreasing the RHS from 5 to 0) will change the objective value (profit) by -(-7.84) (positive direction)
So, optimal profit will increase by 7.84*5 = $ 39.2
Yes, it changes the optimal decision variables as well. Value of Bride dream decision variable will decrease to 0 and values of other decision variables will increase.
d. Shadow price of Mixing is 3.8 and of Final design is 12.6
Allowable decrease for mixing is 2.25 and allowable increase for Final design is 2.25
Sum of percent of change as ratio of allowable limit = 1/2.25+1/2.25 = 0.89 or 89 %
This is less than 100 % , therefore, shadow prices are applicable.
Change in profit = Shadow price of Mixing * Change in RHS value + Shadow price of Final design * Change in RHS value
= 3.8*(-1) + 12.6*1 = 8.8
Objective value (profit) will increase by $ 8.8
Optimal decision variable values will also change. Model needs to be re-run to determine the new optimal decision variable values.
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