document.write( "Question 906178: A health club currently charges its 2,000 clients monthly membership dues of $45. The board of directors decides to increase the monthly membership dues. Market research shows that each $1 increase in dues will result in the loss of 7 clients. How much should the club charge each month to optimize the revenue from monthly dues? \n" ); document.write( "
Algebra.Com's Answer #549863 by ankor@dixie-net.com(22740)\"\" \"About 
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A health club currently charges its 2,000 clients monthly membership dues of $45.
\n" ); document.write( " The board of directors decides to increase the monthly membership dues.
\n" ); document.write( " Market research shows that each $1 increase in dues will result in the loss of 7 clients.
\n" ); document.write( " How much should the club charge each month to optimize the revenue from monthly dues?
\n" ); document.write( ":
\n" ); document.write( "let x = no. or dollar increases
\n" ); document.write( "and
\n" ); document.write( "7x = no. clients lost
\n" ); document.write( ":
\n" ); document.write( "Rev = f(x)
\n" ); document.write( "f(x) = (45 + x) * (2000-7x)
\n" ); document.write( "FOIL
\n" ); document.write( "f(x) = 90000 - 315x + 2000x - 7x^2
\n" ); document.write( "f(x) = 90000 + 1685x - 7x^2
\n" ); document.write( "As quadratic equation where a = -7 and b = 1685 the axis of symmetry will give the max revenue x = -b/(2a)
\n" ); document.write( "x = \"%281685%29%2F%282%2A-7%29\"
\n" ); document.write( "x = +120.357 ~ 120
\n" ); document.write( ":
\n" ); document.write( "Max revenue when: 120 + 45 = $165 a month with
\n" ); document.write( "2000 - 7(120) = 842 clients
\n" ); document.write( "Rev then: 842 * 165 = $138,930\r
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "
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