document.write( "Question 856622: The cost C (in dollars) of manufacturing x wheels at Deon's Bicycle Supply is given by the function C(x)= 0.1x^2-60x+22,744. What is the minimum cost of manufacturing wheels? Do not round your answer. \n" ); document.write( "

Algebra.Com's Answer #516083 by josmiceli(19441) $\"\"$ $\"About$

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$\"+C%28x%29+=+.1x%5E2+-+60x+%2B+22744+\"$
\n" ); document.write( "This is a parabola which has a minimum
\n" ); document.write( "Here's the plot:
\n" ); document.write( " $\"+C%28x%29+\"$ is plotted on the y-axis and
\n" ); document.write( "is rescaled to thousands of dollars
\n" ); document.write( " $\"+graph%28+500%2C+500%2C+-100%2C+700%2C+-5%2C+30%2C+.0001x%5E2+-+.06x+%2B+22.744+%29+\"$
\n" ); document.write( "An initial guess would be $\"+C%5Bmin%5D+=+14000+\"$
\n" ); document.write( "---------------------
\n" ); document.write( "When the form is:
\n" ); document.write( " $\"+a%2Ax%5E2+%2B+b%2Ax+%2B+c+\"$ , the min ( or max ) is at
\n" ); document.write( " $\"+x%5Bmin%5D+=+-b%2F%282a%29+\"$
\n" ); document.write( " $\"+a+=+.1+\"$
\n" ); document.write( " $\"+b+=+-60+\"$
\n" ); document.write( " $\"+-b%2F%282a%29+=+-%28-60%29+%2F+%282%2A.1%29+\"$
\n" ); document.write( " $\"+-b%2F%282a%29+=+60%2F.2+\"$
\n" ); document.write( " $\"+x%5Bmin%5D+=+300+\"$
\n" ); document.write( "Now plug this value of $\"x\"$ back into equation:
\n" ); document.write( " $\"+C%28x%29+=+.1x%5E2+-+60x+%2B+22744+\"$
\n" ); document.write( " $\"+C%28300%29+=+.1%2A300%5E2+-+60%2A300+%2B+22744+\"$
\n" ); document.write( " $\"+C%28300%29+=+9000+-+18000+%2B+22744+\"$
\n" ); document.write( " $\"+C%28300%29+=+13744+\"$
\n" ); document.write( "The minimum cost is $13,744
\n" ); document.write( " \n" ); document.write( "

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