a. The equipment used for peeling and cutting must be replaced. The new equip- ment will have a capacity of only 1,200 minutes. What impact will this change have on the optimal values of the decision variables and on profit?

b. What would the unit profit on the Florida mix have to be before it would become profitable to produce?

c. If management had a choice of obtaining more oranges or more pineapples, which one should be chosen? Why?

d. Management has just learned that an additional 50 pounds of pineapples are on hand. What will the optimal values of the decision variables change to?

e. Management is considering making changes that will cause the profit on the Hawaiian mix to be $8 per unit. Would this affect the solution? Will it affect the optimal value of the objective function?

f. Management is considering a change in equipment that would result in increasing the profit on the Hawaiian mix to $8 per unit but result in decreasing the profit on the California mix by $1. Would these changes be within the range of optimality? If so, how much would the optimal profit change?

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A firm produces jars of chilled fruit that are sold to restaurants. Three varieties of fruit are sold: California mix (x1), Florida mix (x2), and Hawaiian (x3). Each of the three fruit mixes are made by mixing oranges, grapefruit, and pineapple. A linear programming model for the process is Max 4x1 + 3 x2 + 6 x3 s.t. Sensitivity Report: Adjustable Cells Constraints Oranges: Grapefruit Pineapple: Peeling/cutting: Mixing/packaging: Cell Name $B$3 California Mix (x1) $C$3 Florida Mix (x2) $D$3 Hawaiian Mix (x3) Cell Name SE$8 Oranges LHS $E$9 Grapefruit LHS $E$10 Pineapple LHS $E$11 Peeling/cutting LHS $E$12 Mixing/packaging LHS True False 3 x + 2 x2 + 1 x ≤ 920 pounds 2 x₁ + 2x2+2x3 s 900 pounds 1x: + 2 x2 +3 x3 s 930 pounds 1.2x1 +1.4x2+1.5 x3 ≤ 1,260 minutes 1x1 +2 x2 +1 x 600 minutes X1, X2, X3 20 Final Reduced Objective Allowable Allowable Value Cost Coefficient Increase Decrease 210 0 240 0 ?? 0 870 900 930 612 450 4 3 6 0 1.5 1 0 ?? Final Shadow Constraint Allowable Allowable Value Price R.H. Side Increase Decrease 1E+30 25 420 1E+30 1E+30 2 ?? 6 920 900 930 1260 600 2 1E+30 2 50 280 50 648 150 Use the sensitivity report to answer the following question Currently, we can see that the company produces no Florida Mix. To produce at least some Florida Mix, the company would have to increase its price by at least $1.5 per jar. A firm produces jars of chilled fruit that are sold to restaurants. Three varieties of fruit are sold: California mix (x1), Florida mix (x2), and Hawaiian (x3). Each of the three fruit mixes are made by mixing oranges, grapefruit, and pineapple. A linear programming model for the process is Max 4x1 + 3 x2 + 6 x3 s.t. Sensitivity Report: Adjustable Cells Constraints Oranges: Grapefruit Pineapple: Peeling/cutting: Mixing/packaging: Cell Name $B$3 California Mix (x1) $C$3 Florida Mix (x2) $D$3 Hawaiian Mix (x3) Cell Name SE$8 Oranges LHS $E$9 Grapefruit LHS $E$10 Pineapple LHS $E$11 Peeling/cutting LHS $E$12 Mixing/packaging LHS True False 3 x + 2 x2 + 1 x ≤ 920 pounds 2 x₁ + 2x2+2x3 s 900 pounds 1x: + 2 x2 +3 x3 s 930 pounds 1.2x1 +1.4x2+1.5 x3 ≤ 1,260 minutes 1x1 +2 x2 +1 x 600 minutes X1, X2, X3 20 Final Reduced Objective Allowable Allowable Value Cost Coefficient Increase Decrease 210 0 240 0 ?? 0 870 900 930 612 450 4 3 6 0 1.5 1 0 ?? Final Shadow Constraint Allowable Allowable Value Price R.H. Side Increase Decrease 1E+30 25 420 1E+30 1E+30 2 ?? 6 920 900 930 1260 600 2 1E+30 2 50 280 50 648 150 Use the sensitivity report to answer the following question Currently, we can see that the company produces no Florida Mix. To produce at least some Florida Mix, the company would have to increase its price by at least $1.5 per jar.

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a If the equipment used for peeling and cutting must be replaced with a new equipment that has a capacity of only 1200 minutes then the optimal values ... View the full answer