Consider Figure 4.20, which shows the Sensitivity Report for the Burn-Off Diet Drink example in Section 4.7. For each of the situations described below, check to see if the 100% rule can be used to determine the impact of the simultaneous changes described. If so, compute the total change in cost. Each question is independent of the other questions.

(a) The cost of ingredient B increases by $0.05, and the cost of ingredient A increases by $0.05.

(b) The cost of ingredient C decreases by $0.02, and the chemical Y requirement increases by 30.

(c) The cost of ingredient A increases by $0.02, and the cost of ingredient D increases by $0.03.

(d) The chemical X requirement decreases by 3, the chemical Y requirement increases by 1, and the chemical Z max limit increases by 6.

(e) The daily dosage minimum decreases by 1, and the daily dosage maximum decreases by 3.

(f) The daily dosage maximum increases by 20, and the chemical X requirement increases by 35.

Figure 4.20

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Reduced cost shows Microsoft Excel 14.0 Sensitivity Report Worksheet: (Figure 4.19.xlsx]Burn-Off Diet Drink increase in total cost if ingredient B is used. Variable Cells Final Reduced Objective Allowable Allowable Value 10.250 0.000 4.125 21.625 Cell Name Cost SB55 Number of ounces Ingr A SCS5 Number of ounces Ingr B SDS5 Number of ounces Ingr C SESS Number of ounces Ing D Coéfficient Increase Decrease 0.400 0.200 0.600 0.300 0.000 0.061 0.250 0.069 0.000 1E+30 1.500 0.086 0.069 0.073 0.000 1E+30 Constraints Infinity Shadow Constraint Allowable Allowable Price 0.375 0.088 0.000 -0.024 0.000 Final R.H. Side Increase Decrease 36.00 280.000 200.000 Cell Name Value SFS8 Daily dosage minimum SF$9 Chemical X requirement SF$10 Chemical Y requirement SFS11 Chemical Z max limit SFS12 Daily dosage maximum 36.000 280.000 205.750 1050.000 36.000 16.500 41.000 5.750 47.143 1E+30 1.278 11.000 1E+30 1050.000 346.000 40.000 4.000 The shadow price for chemical X is positive, indicating that total cost increases as the requirement for chemical X increases The shadow price shows amount of decrease in total cost if chemical Z's limit is increased.