An espresso stand finds that its weekly profit is a function of the price, $x$, it charges per cup. If $x$ is in dollars, the weekly profit is $P(x)=-3600 x^2 + 9360 x - 4422$ dollars.

(a) What is the maximum weekly profit. $ help (numbers) (Round to the nearest cent and do not include any commas in your answer.)

(b) What price per cup that produces that maximum profit? $ help (numbers) (Round to the nearest cent.)

(c) Which of the two functions below gives a function that has the same maximum profit?
A. $P(x) - 3$
B. $P( x-3)$

(d) Based on the function in your answer to (c) above, what price per cup of produces that maximum profit? $ help (numbers) (Round to the nearest cent.)

(e) Which of the two functions below gives gives a function where the price per cup that produces the maximum profit remains unchanged?
A. $P(x+80)$
B. $P(x)+80$

(f) Based on the function in your answer to (e) above, what is that maximum weekly profit? $ help (numbers) (Round to the nearest cent.)