Question

You are the operations manager of Spartan Ice Cream Shoppe that produces its own ice cream. You make and sell five flavors; Vanilla (v), Chocolate (c), Pistachio (p), Banana (b) and Rocky Road (rr). You want to make as much money as you can, of course. The profits per gallon for the five flavors are Vanilla: $40, Chocolate: $55, Pistachio: $70, Banana: $75 and Rocky Road: $90. You can make up to 200 gallons. You have to make at least 10 gallons of each flavor and you cannot make more than 75 gallons of any one flavor. How many gallons of each ice cream should you make? Assume you sell all of the ice creams you make. 1. What objective are you trying to optimize? (1 pt) (cost, profit, ice cream, or gallon) profits 2. Are you maximizing, minimizing or hitting a target for that objective? (1 pt) (provide your answer exactly as the bold words) ma 3. What is/are the decision variable(s)? (2 pts) (provide your answer in the format of "the number *** of ***) the number gallons of ice cream 4. What is/are the input variables (parameter/coefficient values used in the objective function)? (2 pts) Vanilla, pistachio, chocolate, banana and Rocky Road 5. What is the formula for what you are trying to optimize? (2 pts) max z 6. What is/are the constraint(s)? (2 pts) 7. What is/are the formula(s) for the constraint(s)? (2 pts) 8. Extra Credit: What is the solution for this problem? (+2 pts) $24,750

Answer 1

Hi,

Please find answer as below.

I have used excel solver to solve the problem. I have attached the screen shot of Input Data, Formulas and Constraints used along with the optimal solution for the reference.

Answer

Answers Xi = No. of X2 No. ot X3 = No. of XY = No. of 1 XS = No. of gallons of Vanilla produced gallons of chocolate produced gallons of pistachio produced gallons of banana produeed. gallons of rocky rood produced. - objective function is to maximize the total ---- poolt la Bi Type of ice cream protit per gallen Vanilla 40 chocolate $ 55 Pistachio Banana $75 Rocky road. - objective function = max. protit L Max Pront = 4004 + 5502 + 70 X3 + 75 84 + 90 85 - constraints. 4 > 10 X2 », l X3 3,10 Xų > 10 XS), 10 X1275 e X2 LAS X3575 Xu E75 X5 275 Scanned with CamScanner

Ans objective is to optimile to poubit Ans: 2 . maximizing the profit X, X2, X3, Xn, X5 decision And 13 1 vaniables. Ans: 4 co-efficient values rused in objectice funetin : . XI X2 x3 xy X5 40 55 70 25. = = 1 • Ans. 5 тох 2. 4ox, FГ Х} }o X3 FTX; + 90X5 Ansit Construint. X1.710 X2 >10 X3 & 10 ху >10 XI Str. X2 575 X3 Et x 53г Scanned with CamScanner

Solution

Max Profit = $ 24,750 by producing 75 gallons of each type of ice cream.

1. Snapshot of Input Data

A B Ice Cream Type Profit per Gallon Vanilla $ 40.00 Chocolate $ 55.00 Pistachiio $ 70.00 Banana 75.00 Rocky Road $ 90.00 Max Profit $ Ice Cream Type Gallons Produced Vanilla Chocolate Pistachio Banana Rocky Road

2. Snapshot of Formulas used

A B C Ice Cream Type Profit per Gallon Vanilla Chocolate Pistachiio Banana Rocky Road 90 Max Profit =SUMPRODUCT(D5:09,D15:D19) Ice Cream Type Gallons Produced Vanilla Chocolate Pistachiio Banana Rocky Road

​​​​​​​3. Snapshot of Constraints used

Show Queries From Table Get External Data New Query - Lo Recent Sources Get & Transform 91 Connections Properti Solver Parameters Refresh All Edit Lind Connections Set Objective: SD$12 To: Max Min O Value Of: By Changing Variable Cells: SD$15:50519 A B Subject to the Constraints: $D$15:$D$19 <= 75 $D$15:$D$19 >= 10 Add Change Delete Ice Cream Type Profit per Gallon Vanilla 40.00 Chocolate $ 55.00 Pistachiio $ 70.00 Banana $ 75.00 Rocky Road $ 90.00 Reset All Load/Save Make Unconstrained variables Non-Negative Max Profit $ Select a Solving Method: Simplex LP Options Ice Cream Type Gallons Produced Vanilla Chocolate Pistachio Banana Rocky Road Solving Method Select the GRG Nonlinear engine for Solver Problems that are smooth nonlinear. Select the LP Simplex engine for linear Solver Problems, and select the Evolutionary engine for Solver problems that are non-smooth. Help Solve Close

​​​​​​​4. Snapshot of Optimal Solution

Ice Cream Type Profit per Gallon Vanilla $ 40.00 Chocolate $ 55.00 Pistachio $ 70.00 Banana $ 75.00 Rocky Road $ 90.00 Max Profit $ 24,750.00 Ice Cream Type Gallons Produced Vanilla Chocolate Pistachio Banana Rocky Road