Refer to question 8.

Solution:

Let the fruit grower use x bags of brand P and y bags of brand Q.

The problem can be formulated as follows.

Maximize $z=3 x+3.5 y$                 (1)

subject to the constraints,

$x+2 y \geq 240$                            (2)

$x+0.5 y \geq 90$                           (3)

$1.5 x+2 y \leq 310$                       (4)

$x, y \geq 0$                                  (5)

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

The corner points are A (140, 50), B (20, 140), and C (40, 100).

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

The maximum value of z is 595 at (140, 50).

Thus, 140 bags of brand P and 50 bags of brand Q should be used to maximize the amount of nitrogen.

The maximum amount of nitrogen added to the garden is 595 kg.