The utility function of a firm is given by U(q) = -q2 + 80q + 25,300 (dollars). Determine the maximum utility.

$$ U^{\prime}\left(q\right)=\frac{d}{dq}(-q^2+80q+25300) $$ $$ U^{\prime}\left(q\right)=-2q+80 $$ U'(q)=0 -2q+80=0 q=40 $$ U^{\doubleprime}\left(q\right)=-2>0 $$ Maximum Utility, $$ U\left(40\right)=-2\cdot40^2+80\cdot40+25300=25300 $$