| Maximum \(\bf P\) | ||
|---|---|---|
| \(L_{1}:\quad 0\le x \le 6, y=0\) | \(P(x,0)= -3x^{2}+12x\) | \(P(2,0)=12\) |
| \(L_{2}:\quad x=6, x \le y \le 20\) | \(P(6,y)= -3y^{2}+8y -36\) | \(P(6,y)<0\) |
| \(L_{3}:\quad 0\le x \le 6, y= 20\) | \(P(x,20)= -3x^{2}-28x -800\) | \( P(x,20)<0\) |
| \(L_{4}:\quad x=0, 0 \le y \le 20\) | \(P(0,y)= -3y^{2}+20y\) | \(P(0,\frac{10}{3}) =33.33\) |
| Critical point (1, 3): | \(P(1,3) =36\) |