Question

maximize P=9x+9y Subject to 2x+y is less than or equal to 30 x+2y is less than or equal to 24 x, y is greater than 0 What is the maximum value of P? (integer or fraction)

Answer 1

Find the intersection point between the 2 restraint equations:
$30 - 2x = 12 - \frac{1}{2} x \\ \frac{3}{2} x = 18 \\ x = 12$

Substitute back in to find y-value:
$y = 30 - 2(12) = 6$

P is maximized at point (12,6)
$P = 9(12)+9(6) = 162$