A restaurant chain is considering raising the prices on their burgers. They have found that for every $ 1 increase, their customers will buy 50 fewer burgers each day. Say that the price of a burger is currently $ 9, and their customers buy 850 burgers per day.
a) Write a formula $p(x)$, which gives the price per burger (in dollars) after an increase of $x$ dollars per burger.
$p(x)=$

b) Write a formula $k(x)$, which represents the number of burgers the chain sells each day after an increase of $x$ dollars per burger.
$k(x)=$

c) Which of the following gives an interpretation of $p(x) \cdot k(x)$ in real-world terms.

A. $p(x)\cdot k(x)$ gives the daily revenue of the restaurant after an increase of $x$ dollars per burger.

B. $p(x)\cdot k(x)$ gives the daily profit of the restaurant after an increase of $x$ dollars per burger.

C. $p(x)\cdot k(x)$ gives the increase in profit after an increase of $x$ dollars per burger.

D. $p(x)\cdot k(x)$ gives the total price of a burger after an increase of $x$ dollars per burger.

d) Find the approximate value of $x$ which maximizes $p(x) \cdot k(x)$.
$x=$ dollars

Hint: