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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 $P(x)=?3100x_{2}+11470x?8905.75$ dollars. (a) What is the maximum weekly profit. \$ (Round to the nearest cent and do not include any commas in your answer.) (b) What price per cup that produces that maximum profit? \$ (Round to the nearest cent.) (c) Which of the two functions below gives a function that has the same maximum profit? A. $P(x)?2$ B. $P(x?2)$ (d) Based on the function in your answer to (c) above, what price per cup of produces that maximum profit? \$ (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. $P(x+50)$ B. $P(x)+50$ (f) Based on the function in your answer to (e) above, what is that maximum weekly profit? \$ (Round to the nearest cent.)

Given profit functionP(x)=?3,100x2+11,470x