The maximum profit is the y-coordinate of the vertex of the parabola represented by the equation.
\(P(c)=-20c^2+320c+5120 \\ \\
a=-20 \\
b=320 \\ \\
\hbox{the vertex } (h,k): \\
h=\frac{-b}{2a}=\frac{-320}{2 \times (-20)}=\frac{-320}{-40}=8 \\
k=f(h)=f(8)=-20 \times 8^2+320 \times 8+5120= \\
=-1280+2560+5120=6400\)
The maximum value is 6400, but the profit is given in hundreds of dollars, so multiply the value by 100.
The maximum profit the company can make is $640,000.
