# how we can initiate the graph and how can we solve the question of linear programming graphically  when this type of question come in 6 marks?

Hi!

Consider a linear programming problem.

A manufacturer produces nuts and bolts. It takes 1 hour of work on machine A and 3 hours on machine B to produce a package of nuts. It takes 3 hours on machine A and 1 hour on machine B to produce a package of bolts. He earns a profit, of Rs 17.50 per package on nuts and Rs. 7.00 per package on bolts. How many packages of each should be produced each day so as to maximize his profit, if he operates his machines for at the most 12 hours a day?

Solution:
Firstly read the problem carefully and analyze the situation.
The manufacturer needs to manufacture packages of nuts and bolts to maximize his profit.
The manufacturer first to identify the decision variables i.e., number of packages of nuts and bolts to be manufactured to maximize the profit.
The corner points of the feasible region are are A (4, 0), B (3, 3), and C (0, 4).

The values of Z at these corner points are as follows.

 Corner point Z = 17.5x + 7y O(0, 0) 0 A(4, 0) 70 B(3, 3) 73.5 → Maximum C(0, 4) 28

The maximum value of Z is Rs 73.50 at (3, 3).

Thus, 3 packages of nuts and 3 packages of bolts should be produced each day to get the maximum profit of Rs 73.50.

Cheers!

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