Question

1.a juice company has available two kinds of food juices: orange... 1. a juice company has available two kinds of food juices: orange juice and grape juice. the company produces two types of punches: punch a and punch b. one bottle of punch a requires 20 liters of orange juice and 5 liters of grape juice.1 bottle of punch b requires 10 liters of orange juice and 15 liters of grape juice. from each of bottle of punch a a profit of $4 is made and from each bottle of punch b a profit of $3 is made .suppose that the company has 230 liters of orange juice and 120 liters of grape juice available required: a. formulate this problem as a lpp(1 point) b. how many bottles of punch a and punch b the company should produce in order to maximize profit? (using the simplex method)(8 point) c. what is this maximum profit?(1 point)

Answer 1

The juice company have a maximized profit of $51 when they produce 9 bottles of Punch A and 5 bottles of Punch B

The linear programming model of the problem

The following table represents the given parameters

               Punch A (x)    Punch B (y)       Available

Orange       20                10                       230

Grape          5                 15                        120

Profit            4                 3

From the above table, the linear programming models are:

Objective function: Max P = 4x + 3y

Constraints

20x + 10y ≤ 230

5x + 15y ≤ 120

x , y ≥ 0

The bottles to be produced by the company

To do this, we plot the graph of the constraints

See attachment for the graph of the constraints

Where we have:

• Punch A (x) = 9
• Punch A (y) = 5

This means that the company have to produce 9 bottles of Punch A and 5 bottles of Punch B for profit to be maximized

The maximum profit?

In (b), we have:

x = 9 and y = 5

Substitute these values in P = 4x + 3y

P = 4 * 9 + 3 * 5

P = 51

Hence, the maximum profit of the company is $51

Read more about objective functions at:

brainly.com/question/16826001

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