A Fast-Food Restaurant Determines the Cost Model $C = 0.6 x + 5500,0 \leq x \leq 40000$

Multiple Choice

A fast-food restaurant determines the cost model, $C = 0.6 x + 5500,0 \leq x \leq 40000$ and revenue model, $R = \frac { 1 } { 30000 } \left( 55000 x - x ^ { 2 } \right)$ for $0 \leq x \leq 40000$ where x is the number of hamburgers sold. Determine the intervals on which the profit function is increasing and on which it is decreasing.

A) The profit function is increasing on the interval $( 18500,40000 )$ and decreasing on the interval $( 0,18500 )$ .
B) The profit function is increasing on the interval $( 0,12500 )$ and decreasing on the interval $( 12500,40000 )$ .
C) The profit function is increasing on the interval $( 0,18500 )$ and decreasing on the interval $( 18500,40000 )$ .
D) The profit function is increasing on the interval $( 12500,40000 )$ and decreasing on the interval $( 0,12500 )$ .
E) The profit function is increasing on the interval $( 0,5500 )$ and decreasing on the interval $( 5500,40000 )$ .