Variable Cells Final Reduced Objective Allowable Allowable Cell Name Value Cost
ID: 357683 • Letter: V
Question
Variable Cells Final Reduced Objective Allowable Allowable Cell Name Value Cost Coefficient Increase Decrease? SB$4 Nuggets 75 0 SC$4 Mini-nuggets01.5 0 1.5 1E+30 C 9 SDS4 Chips 75 6 0.6 Constraints Final Shadow Constraint Allowable Allowable Cellame Value Price R.H. Side Increase Decrease 50 75 105 30 SES7 Bark 600 1.5 600 150 1E+30 1E+30 SE$8 Machine 525O600 E$9 Labor SES10 Storage 375 0 480 150 15150: 7.894736842 a. How many of each type of product should be prepared and what is the maximunm profit? b. Which variables are basic and which are non-basic? c. A new competitor entered the market providing Chips with a competitive price, the manager decided to decrease the profit contribution of Chips by 0.6. What is the effect of the manager decision? d. If the profit on the Mini-Nuggets increases to 10, will any of the Mini-Nuggets be prepared? Explain. e. Calculate the range of optimality of Nuggets and interpret the result. f. Which constraints ar g. Which one of the three products will have the highest increase in profit for each Explain.Constraint dollar increase in profit contribution?Explanation / Answer
a) From the final value in variable cells, we get to know the quantity and type to be prepared.
Nuggets = 75
Chips = 75
Profit maximum = 75*9+(75*6) = 1125 [ prices are taken from the objective coefficient]
b) Nuggets and Chips are basic variables as tehy are need to be prepared and mini nuggets is non basic variable as the quantity is zero for that.
c) Nothing will happen as the objective function wont get affected by the manager's decision because the allowable decrease is 0.6 for chips objective coefficient.
d) No. We have to increase the price of the mini nuggets by 1.5 to make itself enable to be prepared.
e) Optimality:
8<=Nuggets<=10
Mini nuggets >=10.5
5.4<=Chips<=9
f) Bark and storage constraints are binding as they have final value equal to the constraint right hand side and also they do have the shadow price.
g) Nuggets will have the highest profit contribution as the objective coefficient is already nine and when it gets increased to 10, profit will grew at higher rate than the chips.
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