document.write( "Question 180438: The number of units, n, of a commodity sold at price ,p, is given by n= -0.2p + 50. The revenue is the product of the selling price and the number of units sold. The maximum revenue for this commodity is? \n" ); document.write( "
Algebra.Com's Answer #135316 by ankor@dixie-net.com(22740)\"\" \"About 
You can put this solution on YOUR website!
The number of units, n, of a commodity sold at price ,p, is given by n = -0.2p + 50. The revenue is the product of the selling price and the number of units sold. The maximum revenue for this commodity is?
\n" ); document.write( ":
\n" ); document.write( "We know that revenue = no. of units (n) times the price (p)
\n" ); document.write( "so we have:
\n" ); document.write( "r = p * n
\n" ); document.write( "given that n = -.2p + 50, substitute this for n
\n" ); document.write( "r = p * (-.2p = 50)
\n" ); document.write( ":
\n" ); document.write( "r = -.2p^2 + 50p; a quadratic equation
\n" ); document.write( ";
\n" ); document.write( "The max revenue occurs at the axis of symmetry, find it using: x = -b/(2a)
\n" ); document.write( "p = x, a =-.2, b = 50
\n" ); document.write( "p = \"%28-50%29%2F%282%2A-.2%29\"
\n" ); document.write( "p = \"%28-50%29%2F%28-.4%29\"
\n" ); document.write( "p = +125 price for max rev
\n" ); document.write( ":
\n" ); document.write( "Find the max rev by substituting 125 for p
\n" ); document.write( "r = -.2(125^2) + 50(125)
\n" ); document.write( "r = -.2(15625) + 6250
\n" ); document.write( "r = -3125 + 6250
\n" ); document.write( "r = $3125 max revenue
\n" ); document.write( ";
\n" ); document.write( "Did this make sense to you now? \n" ); document.write( "
\n" );