Answer :

let x and y be the number of toys manufactured per day of type A and B respectively. Obviously x ≥ 0, y ≥ 0. Mathematical formulation of given problem is as follows:


Maximize Z = 7.5x + 5y ….(1)


Subject to the constraints,


2x + y ≤ 60 …..(2)


x ≤ 60 …..(3)


2x + 3y ≤ 120 ….(4)


x ≥ 0, y ≥ 0 ….(5)


Now let us graph the feasible region of the system of inequalities (2) to (5). The feasible region (shaded) is shown in the fig. Here, we can observe that the feasible region is bounded.



The coordinates of the corner points A(20,0),B(20,20), C(15,30)and D(0,40).



Now, we find the maximum value of Z. According to table the maximum value of Z = 262.5 at point C (15,30).


Hence, 15 and 20 be the number of toys manufactured per day of type A and B respectively to get the maximum profit.


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