document.write( "Question 337287: Aki's Bicycle Designs has determined that when x hundred bicycles are built, the average cost per bicycle is given by C(x)=0.5x^2-0.6x +3.659 where C(x) is in hundreds of dollars. How many bicycles should the shop build to minimize the average cost per bicycle?
\n" ); document.write( "The shop should build ______ bicycles. \n" ); document.write( "
Algebra.Com's Answer #242115 by nyc_function(2741)\"\" \"About 
You can put this solution on YOUR website!
This may not be the exact answer or correct reason, you can compare the results with other answers.\r
\n" ); document.write( "\n" ); document.write( "Solving your quadratic equation using standard formula gives imaginary roots for x.
\n" ); document.write( "i.e. x = (0.6 + i2.6) or x = (0.6 - i2.6)\r
\n" ); document.write( "\n" ); document.write( "Considering the second requirement, i.e the cost C(x) to be minimum, take first derivative of the equation and evaluate to zero. This gives,\r
\n" ); document.write( "\n" ); document.write( "dC(x)/dx = 0.5*2*x - 0.6 = 0
\n" ); document.write( "x = 0.6
\n" ); document.write( "This means 0.6 * 100 = 60 bicycles.\r
\n" ); document.write( "\n" ); document.write( "Verify the result:
\n" ); document.write( "For x = 60, C(x) = 1768 dollars. Avg = $29.45
\n" ); document.write( "For x = 70, C(x) = 2411 dollars. Avg = $34\r
\n" ); document.write( "\n" ); document.write( "For x = 50 or less, the Avg values are lesser than $29.45. I hope this helps.
\n" ); document.write( " \n" ); document.write( "
\n" );