Refer to Example 9. How many packets of each food should be used to maximize the amount of vitamin A in the diet? What is the maximum amount of vitamin A in the diet?
Let the diet contain x and y packets of foods P and Q respectively. Therefore,
$x \geq 0$ and $y \geq 0$
The mathematical formulation of the given problem is as follows.
Maximize $z=6 x+3 y$
subject to the constraints,
$4 x+y \geq 80$ (1)
$x+5 y \geq 115$ (2)
$3 x+2 y \leq 150$ (3)
$x, y \geq 0$ (4)
The feasible region determined by the system of constraints is as follows.