(1 point)
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 $\$ 4$, 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.
\[
p(x)=\square
\]
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.
\[
k(x)=\square
\]
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 4 ter 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 $p(x) \cdot k(x)$.
\[
x=\square \text { dollars }
\]
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