document.write( "Question 919163: 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)=−3000x2+11400x−9252 dollars. \r
\n" ); document.write( "\n" ); document.write( "(a) What is the maximum weekly profit. $______ (Round to the nearest cent)\r
\n" ); document.write( "\n" ); document.write( "(b) What price per cup that produces that maximum profit? $ _____ (Round to the nearest cent.)
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Algebra.Com's Answer #557558 by lwsshak3(11628) $\"\"$ $\"About$

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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)=−3000x2+11400x−9252 dollars.
\n" ); document.write( "(a) What is the maximum weekly profit. $______ (Round to the nearest cent)
\n" ); document.write( "(b) What price per cup that produces that maximum profit? $ _____ (Round to the nearest cent.)
\n" ); document.write( "***
\n" ); document.write( "P(x)=−3000x2+11400x−9252
\n" ); document.write( "complete the square:
\n" ); document.write( "P(x)=−3000(x^2-3.8x+(3.8/2)^2)+3000*(1.9)^2−9252
\n" ); document.write( "=-3000(x-1.9)^2+10830-9252
\n" ); document.write( "=-3000(x-1.9)^2+1578
\n" ); document.write( "This is an equation of a parabola that opens up with vertex at (1.9,1578)
\n" ); document.write( "(a) What is the maximum weekly profit? $1578
\n" ); document.write( "(b) What price per cup that produces that maximum profit? $1.90 \n" ); document.write( "

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