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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
B, How many bottles of Punch A and Punch B the company should produce in order to maximize profit?
C, What is this maximum profit? ​

Sagot :

MrRoyalidn

The company should produce 9 bottles of Punch A and 5 bottles of Punch B in order to have a maximized profit of $51

Formulate the problem as a linear programming

The given parameters can be represented using the following table:

                Punch A (x)    Punch B (y)       Available

Orange       20                10                       230

Grape          5                 15                        120

Profit            4                 3

From the above table, we have:

Objective function: Max P = 4x + 3y

Subject to:

20x + 10y ≤ 230

5x + 15y ≤ 120

x , y ≥ 0

Bottles of Punch A and Punch B the company should produce

To do this, we plot the graph of the constraints

From the graph (see attachment), we have:

Punch A (x) = 9

Punch A (y) = 5

Hence, the company should produce 9 bottles of Punch A and 5 bottles of Punch B in order to maximize profit

What is this maximum profit? ​

Substitute 9 for x and 5 for y in P = 4x + 3y

This gives

P = 4 * 9 + 3 * 5

Evaluate

P = 51

Hence, the maximum profit of the company is $51

Read more about objective functions at:

https://brainly.com/question/16826001

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View image MrRoyal
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