Answer :

Let the company manufacturer x souvenirs of type A and y souvenirs of type B

∴ x and y ≥ 0

The tabular representation of the given data is:

The profit on type A souvenirs is Rs 5 and that on type B souvenirs is Rs 6.

The constraints here are of the form:

5x+ 8y ≤ 200

And 10x+ 8y ≤ 240 or 5x + 4y ≤ 120

The function is to maximize the profit Z = 5x+ 6y

The mathematical formulation of the data

Maximise Z = 5x+ 6y

Subject to constraints

5x+ 8y ≤ 200

5x + 4y ≤ 120

x and y ≥ 0

The feasible region is determined by the system of constraints is as follows:

The corner points here are A( 24, 0) , B( 8, 20) and C( 0 , 25)

The value of Z at these corner points are :

The maximum value of Z is at the point (8, 20)

Thus the firm should produce 8 number of souvenirs of type A and 20 type B souvenirs each day in order to maximize its profit of Rs160.

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