document.write( "Question 1097010: A health club currently charges its 1900 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 3 clients. How much should the club charge each month to optimize the revenue from monthly dues? \n" ); document.write( "
Algebra.Com's Answer #711453 by ankor@dixie-net.com(22740)\"\" \"About 
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A health club currently charges its 1900 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 3 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. of $1 increases, and -3x = the no. of client decreases
\n" ); document.write( "Revenue = price * no. of clients
\n" ); document.write( "R(x) = (45 + x)(1900 - 3x)
\n" ); document.write( "FOIL
\n" ); document.write( "R(x) = 85500 - 135x + 1900x - 3x^2
\n" ); document.write( "a quadratic equation
\n" ); document.write( "y = -3x^2 + 1765x + 8550
\n" ); document.write( "The max y (revenue) occurs on the axis of symmetry. x = -b/(2a)
\n" ); document.write( "x = \"%28-1765%29%2F%282%2A-3%29\"
\n" ); document.write( "x = 294
\n" ); document.write( "Max revenue occurs when 294 + 45 = $339 a month are the dues
\n" ); document.write( "then the no. of clients: 1900 - 3(294) = 1018 clients
\n" ); document.write( ":
\n" ); document.write( ":
\n" ); document.write( "Not a realistic scenario! \n" ); document.write( "
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