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Gillian’s Restaurant has an ice-cream counter where it sells two main products, ice cream and frozen yogurt, each in a variety of flavors. The restaurant makes one order for ice cream and yogurt each week, and the store has enough freezer space for 115 gallons total of both products. A gallon of frozen yogurt costs $0.75 and a gallon of ice cream costs $0.93, and the restaurant budgets $90 each week for these products. The manager estimates that each week the restaurant sells at least twice as much ice cream as frozen yogurt. Profit per gallon of ice cream is $4.15, and profit per gallon of yogurt is $3.60.

Required:
a. Formulate this problem as a linear program. Make sure to clearly define you variables and label your constraints.
b. Solve this model by using graphical analysis.

Respuesta :

samuelonum1

Answer:

P=$440

Step-by-step explanation:

NOTE: kindly find attached the graphical analysis/solution.

Given the data, we are expected to maximize the profit of Gillian’s Restaurant

let X be icecream

and Y be yogurt

Our objective function is

4.15X+3.6Y=P

Constraints

a. 0.75X+0.93Y<90

b. X+Y<115

c. X>=2Y = X-2Y>=0

X>=0, Y>=0      

 

a. 0.75X+0.93Y=90

X=0  

      0.75(0)+0.93Y=90

       0.93Y=90

                Y=90/0.93

                 Y=96.77

Y=0

       0.75X+0.93(0)=90

       0.75X=90

                X=90/0.75

                 X=120

b. X+Y<115

    X=0  

               X+Y=115

               0+Y=115

                Y=115

                 

Y=0

        X+0=115

               X+0=115

                X=115

c. X>=2Y = X-2Y>=0

 X=0  

               X-2Y=0

               0+2Y=0

                Y=0

Y=0  

               X-2(0)=0

               X+0=0

                X=0

From the graph profit is maximum at

X=80 and Y=30

4.15(80)+3.6(30)=P

332+108=P

440=P

P=$440

Ver imagen samuelonum1

We are expected to maximize the profit of Gillian’s Restaurant:

let

  • X = icecream
  • Y = yogurt

Objective function =4.15X+3.6Y=P

Constraints

a. 0.75X+0.93Y<90

b. X+Y<115

Part A :

             0.75X+0.93Y=90

X=0  

      0.75(0)+0.93Y=90

      0.93Y=90

      Y=90/0.93

       Y=96.77

Y=0

      0.75X+0.93(0)=90

      0.75X=90

       X=90/0.75

        X=120

Part B:

            X+Y<115

 X=0  

  •               X+Y=115
  •               0+Y=115
  •               Y=115

               

Y=0

  •        X+0=115
  •         X+0=115
  •         X=115

The graph profit is maximum at

X=80 and Y=30

  • 4.15(80)+3.6(30)=P
  • 332+108=P
  • 440=P
  • P=$440

Find out more information about "linear program":

https://brainly.com/question/14161814?referrer=searchResults

Ver imagen Sam1s

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