Find the intersection point between the 2 restraint equations:
[tex]30 - 2x = 12 - \frac{1}{2} x \\ \frac{3}{2} x = 18 \\ x = 12[/tex]
Substitute back in to find y-value:
[tex]y = 30 - 2(12) = 6[/tex]
P is maximized at point (12,6)
[tex]P = 9(12)+9(6) = 162[/tex]
