document.write( "Question 979995: You run a canoe-rental business on a small river in Ohio. You currently charge $12 per canoe and average 36 rentals a day. An industry journal says that, for every fifty-cent increase in rental price, the average business can expect to lose two rentals a day. Use this information to attempt to maximize your income. What should you charge? \n" ); document.write( "
Algebra.Com's Answer #601341 by ankor@dixie-net.com(22740)![]() ![]() You can put this solution on YOUR website! You currently charge $12 per canoe and average 36 rentals a day. \n" ); document.write( "An industry journal says that, for every fifty-cent increase in rental price, the average business can expect to lose two rentals a day. \n" ); document.write( "Use this information to attempt to maximize your income. \n" ); document.write( "What should you charge? \n" ); document.write( ": \n" ); document.write( "Let's use x as the variable \n" ); document.write( ".5x = no. of 50 cent increases \n" ); document.write( "and \n" ); document.write( "2x = no. of rentals lost \n" ); document.write( ": \n" ); document.write( "Revenue (r) \n" ); document.write( "r(x)= (12+.5x)*(36-2x) \n" ); document.write( "FOIL \n" ); document.write( "r(x) = 432 - 24x + 18x - x^2 \n" ); document.write( "r(x) = -x^2 - 6x + 432 \n" ); document.write( "Max income occurs at the axis of symmetry, x =-b/(2a) \n" ); document.write( "x = \n" ); document.write( "x = \n" ); document.write( "x = -3, a negative solution means you should lower the price \n" ); document.write( "Charge 12 - 3(.50) = $10.50 for each canoe \n" ); document.write( "Then -2x becomes + 6 \n" ); document.write( "10.50 * 36 + 6 = 42 canoes \n" ); document.write( "max revenue then: 10.50 * 42 = $441 \n" ); document.write( " \n" ); document.write( " |