QUESTION 1 H&S desserts supplies its ice cream shops with three flavors of ice cream: chocolate, vanilla, and banana. In addition to the specific flavors, the main ingredients in the ice creams are milk, sugar, and cream. Due to extreme hot weather and a high demand for its products, the company has run short of its supply of ingredients and will not be able to fill all the orders received from the ice cream stores. The chocolate, vanilla, and banana flavors generate AED 20, 18, and 16 of profit for each gallon sold, respectively. Below is a screenshot of the spreadsheet model that was used to determine how many gallons of ice cream should the company produce of each flavor in order to maximize the total profit, along with its corresponding sensitivity report. Unit Proft (AED) Chocolate Vanilla Banana 20 18 16 Requirements /Gallon of Ice Cream 0.45 0.5 0.4 0.5 0.4 0.4 0.1 0.15 0.2 Milk Sugar Cream Used 187.5 150 56.25 Available 200 150 60 Gallons Produced 0 375 0 Total Profit (AED) 6750 Variable Cells Cell $C$8 $D$8 $E$8 Name Chocolate Vanilla Banana Final Value 0 375 0 Reduced Objective Allowable Allowable Cost Coefficient Increase Decrease -2.5 20 2.5 1E+30 18 1E+30 2 -2 16 2 1E+30 Question Completion Status: Constraints Cell $F$4 $F$5 $F$6 Name Milk Used Sugar Used Cream Used Final Value 187.5 150 56.25 Shadow Constraint Allowable Allowable Price R.H. Side Increase Decrease 0 200 1E+30 12.5 45 150 10 150 0 60 1E+30 3.75 1. Indicate whether the following statements are True (T) or False (F). a) The above represents a resource allocation model with six decision variables b) The constraint associated with gallons of milk used is non-binding because it is underutilized at optimal production level. c) The constraint associated with pounds of sugar used is binding because it is fully utilized at optimal production level. d) The constraint associated with gallons of cream used is binding because it is under-utilized at optimal production level. e) The optimal solution will be impacted if the company increases available gallons of cream to 65 because the constraint is non-binding. f) The optimal solution will be impacted if the company increases its available quantity of sugar to 160 because the constraint is binding. 2. What is the minimum profit per gallon of Vanilla ice cream that would guarantee keeping the optimal daily production of Vanilla ice cream unchanged at 375 gallons? per gallon AED 3. The company is interested in buying an additional pound of sugar. a) What is the maximum price that the company would be willing to pay? AED b) How many more pounds of sugar can be purchased at this price? pounds 4. The company has the opportunity to buy an additional 25 pounds of sugar at a total cost of 300 AED. a) Compute the minimum net profit or loss associated with taking this decision. AED b) Is the value calculated above a profit or loss? 5. The company is considering adding 0.20 gallons of condensed milk to the ingredient for making each gallon of the three types of ice cream, where the total available gallons of condensed milk is 100 gallons per day. Assume that "C", "V", and "B" represent gallons of chocolate, vanilla, and banana ice cream produced, respectively. Indicate whether the following statements are True (T) or False (F). a) The new constraint may be algebraically represented as 0.2 C + 0.2 V +0.2 B >=100 b) The new constraint may be algebraically represented as 0.2 C +0.2 V +0.2 B =100 b) The new constraint may be algebraically represented as 0.2 C +0.2 V +0.2 B
