Answer :

let x and y be the bags of brands P and Q respectively. Obviously x ≥ 0, y ≥ 0. Mathematical formulation of given problem is as follows:

Minimize Z = 3x + 3.5y ….(1)

Subject to the constraints,

x + 2y ≤ 240 …..(2)

3x + 1.5y ≤ 270 x + 0.5y=90 …..(3)

1.5x + 2y ≤ 310 ….(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(140,50),B(20,40) and C(40,100).

Now, we find the minimum value of Z. According to table the minimum value of Z = 470 at point C (40,100).

Hence, 40 and 100 be be the bags of brands P and Q respectively to be added to the garden to minimize the amount of nitrogen.

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