Question

a company producing two products a and b to manufacture a product a certain machine to be utilized for 1.5 hour and a labour time or 2 hours to manufacture a product b the machine has to be utilized 2.5 hours and labor time of 1.5 hours in week the factory can avail 80 hours of machine hrs and 70 hours of labour time the profit on each product a is rs 5 and that product b is rs 4 the manager wishesh to his maximize the profit by consedering all the constaints determine the solution of llp by graphical method..

Answer 1

Answer:

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Answer 2

Answer :

The maximum profit that the company can make subject to the given constraints is Rs. 249.17 by producing 46.67 units of product A and 6.67 units of product B.

Explanation :

To solve this linear programming problem using graphical method, we need to first identify the objective function and constraints.

Objective Function:

Maximize profit = 5A + 4B

Constraints:

1.5A + 2B <= 70 (Labour time constraint)

2.5A + 1.5B <= 80 (Machine time constraint)

A >= 0 (Non-negativity constraint)

B >= 0 (Non-negativity constraint)

Now, we can plot the feasible region by graphing the above constraints on a two-dimensional graph.

First, let's plot the constraint 1.5A + 2B <= 70:

2B <= 70 - 1.5A

B <= 35 - 0.75A

When A = 0, B = 35

When B = 0, A = 46.67

Plotting this on a graph, we get:

    35 |           .

         |        .

         |    .

         |.

         +----------------

            0   46.67

Next, let's plot the constraint 2.5A + 1.5B <= 80:

1.5B <= 80 - 2.5A

B <= 53.33 - 1.67A

When A = 0, B = 53.33

When B = 0, A = 32

Plotting this on the same graph, we get:

   35 |          .

         |      .      .

         |   .            .

         |.

         +----------------

            0   32   46.67

Now, we need to check the feasibility of the corner points of the feasible region. These corner points are the intersection of the two lines we just plotted.

The corner points are:

(0, 35)

(32, 0)

(46.67, 6.67)

We can calculate the profit at each of these corner points using the objective function:

Profit at (0, 35) = 5(0) + 4(35) = 140

Profit at (32, 0) = 5(32) + 4(0) = 160

Profit at (46.67, 6.67) = 5(46.67) + 4(6.67) = 249.17

Therefore, the maximum profit that the company can make subject to the given constraints is Rs. 249.17 by producing 46.67 units of product A and 6.67 units of product B.

To know more about the concept please go through the links :

https://brainly.in/question/35231883

https://brainly.in/question/42891525

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