# A toy company man

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

Maximize Z = 12x + 16y ….(1)

Subject to the constraints,

x + y ≤ 1200 …..(2)

y ≤ x/2 2y ≤ x …..(3)

x – 3y ≤ 600 ….(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(600,0), B(1050,150) and C(800,400).

Now, we find the maximum value of Z. According to table the maximum value of Z = 16000 at point C (800,400).

Hence, 800 and 400 be the number of dolls of type A and B respectively.

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