Solve the Problem $\mathrm { P } ( \mathrm { x } ) = - 4 \mathrm { x } ^ { 2 } + 192 \mathrm { x } - 1904$

Multiple Choice

Solve the problem.
-The daily profit in dollars of a specialty cake shop is described by the function $\mathrm { P } ( \mathrm { x } ) = - 4 \mathrm { x } ^ { 2 } + 192 \mathrm { x } - 1904$ , where $x$ is the number of cakes prepared in one day. The maximum profit for the company occurs at the vertex of the parabola. How many cakes should be prepared per day in order to maximize profit?

A) 24 cakes
B) 2304 cakes
C) 576 cakes
D) 48 cakes