document.write( "Question 378070: If the function C=2x^2-52x+338 can be used to predict the cost of manufactoring x shirts per hour for Company Z, How many shirts should Company Z make per hour if they want to minimize the hourly cost of production? \n" ); document.write( "

Algebra.Com's Answer #268600 by richard1234(7193) $\"\"$ $\"About$

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This problem can be solved using precalculus methods, but the general method to solve such a problem requires calculus. I'll present both solutions:\r
\n" ); document.write( "\n" ); document.write( "Since C is a 2nd degree polynomial, the vertex of the polynomial occurs at $\"x+=+-b%2F2a+=+52%2F4+=+13+%28shirts%29\"$ . The polynomial points upward, therefore 13 is the minimum.\r
\n" ); document.write( "\n" ); document.write( "Or, we may take the derivative of C using the Power Rule: $\"dC%2Fdx+=+4x+-+52\"$ . The derivative equals zero when x = 13, and it can be checked that 13 is the minimum.
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