Question 1 Tom and Jerry, Inc., supplies three flavours of ice cream in their shop: chocolate, vanilla, banana. Due to extremely hot weather and a high demand for its product, the company has decided to choose the amount of each flavour to produce that will maximize total profit, given the constraints on supply of basic ingredients. The chocolate, vanilla, and banana flavours generate, respectively, $2.00, S1.80, and S1.9 of profit per gallon sold. However, the company has only 400 gallons of milk, 300 pounds of sugar, and 120 gallons of cream left in its inventory. A linear programming model has been formulated in a spreadsheet to determine the production levels that would maximize profit. The corresponding sensitivity report is shown below. Variable Cells Cell Name $8$3 Production Chocolate $C$3 Production Vanilla 5053 Production Banana Final Redu Objective Allowable Allowable Value Cost Coefficient increase Decrease 0.07 2 0.075 1E+30 01 0.042 0.1 0.025 Constraints Final Shadow Constraint Allowable Allowable Cell Name Value Price R.H. Side Increase Decrease SESS Milk (gallons) Used 360 SES9 Sugar (pounds) Used 300 1.875 300 20 60 SESTO Cream (gallons) Used 120 1 120 30 75 For each of the following parts, answer the question using the given sensitivity report without re-solving the problem with Solver. Note: Each part is independent (i.e. any change made in one part does not apply to any other parts). (a) What is the optimal solution and total profit? (b) Suppose the profit per gallon of banana increase from $1.9 to $2. Will this change the optimal production quantities? What can be said about the change in total profit? (C) Suppose the profit per gallon of Vanilla decrease to $1.79 and profit per gallon of Banana increase to $1.92. Will this change the optimal production quantities? What can be said about the change in total profit? (d) Suppose the company discovers that six gallons of cream have gone sour and so must be thrown out. Will the optimal solution change and what can be said about the change in total profit? (e) Suppose the company has the opportunity to buy an additional 20 pounds of sugar at a total cost of $15. Should it do so? Explain reason(s). Question 1 Tom and Jerry, Inc., supplies three flavours of ice cream in their shop: chocolate, vanilla, banana. Due to extremely hot weather and a high demand for its product, the company has decided to choose the amount of each flavour to produce that will maximize total profit, given the constraints on supply of basic ingredients. The chocolate, vanilla, and banana flavours generate, respectively, $2.00, S1.80, and S1.9 of profit per gallon sold. However, the company has only 400 gallons of milk, 300 pounds of sugar, and 120 gallons of cream left in its inventory. A linear programming model has been formulated in a spreadsheet to determine the production levels that would maximize profit. The corresponding sensitivity report is shown below. Variable Cells Cell Name $8$3 Production Chocolate $C$3 Production Vanilla 5053 Production Banana Final Redu Objective Allowable Allowable Value Cost Coefficient increase Decrease 0.07 2 0.075 1E+30 01 0.042 0.1 0.025 Constraints Final Shadow Constraint Allowable Allowable Cell Name Value Price R.H. Side Increase Decrease SESS Milk (gallons) Used 360 SES9 Sugar (pounds) Used 300 1.875 300 20 60 SESTO Cream (gallons) Used 120 1 120 30 75 For each of the following parts, answer the question using the given sensitivity report without re-solving the problem with Solver. Note: Each part is independent (i.e. any change made in one part does not apply to any other parts). (a) What is the optimal solution and total profit? (b) Suppose the profit per gallon of banana increase from $1.9 to $2. Will this change the optimal production quantities? What can be said about the change in total profit? (C) Suppose the profit per gallon of Vanilla decrease to $1.79 and profit per gallon of Banana increase to $1.92. Will this change the optimal production quantities? What can be said about the change in total profit? (d) Suppose the company discovers that six gallons of cream have gone sour and so must be thrown out. Will the optimal solution change and what can be said about the change in total profit? (e) Suppose the company has the opportunity to buy an additional 20 pounds of sugar at a total cost of $15. Should it do so? Explain reason(s)