(Solved): A fast-food restaurant determines the cost and revenue models for its hamburgers. \[ \begin{array}{ ...

A fast-food restaurant determines the cost and revenue models for its hamburgers. \[ \begin{array}{l} C=0.7 x+7200, \quad 0 \leq x \leq 50,000 \\ R=\frac{1}{10,000}\left(65,000 x-x^{2}\right), \quad 0 \leq x \leq 50,000 \end{array} \] (a) Write the proft function for this situation. \[ p= \] (b) Determine the intervals on which the profit function is increasing and decreasing. (Enter your answer using interval notation.) increasing decreasing (c) Determine how many hamburgers the restaurant needs to sell to obtain a maximum profit. hamburgers Explain your reasoning. The restaurant makes the same amount of money no matter how many hamburgers are sold. Because the function is always increasing, the maximum profit occurs at this value of \( x \). Because the function changes from decreasing to increasing at this value of \( x \), the maximum profit occurs at this value. Because the function changes from increasing to decreasing at this value of \( x \), the maximum profit occurs at this value. Because the function is always decreasing, the maximum profit occurs at this value of \( x \).