document.write( "Question 294733: The cost in millins of dollars for a company to manufacture x thousand automobiles is given by the function C(x)= 4x^2-16x+32. Find the number of automobiles that must be produced to minimize the cost\r
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\n" ); document.write( "\n" ); document.write( "Tried to factor out the four then simpliy. Stuck. Help! \n" ); document.write( "

Algebra.Com's Answer #212543 by jim_thompson5910(35256) $\"\"$ $\"About$

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The minimum is the C(x) value that is the smallest (ie it is the smallest cost value). This minimum occurs at the vertex (h,k) where \r
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\n" ); document.write( "\n" ); document.write( " $\"h=-b%2F2a\"$ \r
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\n" ); document.write( "\n" ); document.write( "In this case, $\"b=-16\"$ and $\"a=4\"$ meaning that $\"h=-%28-16%29%2F%282%284%29%29=16%2F8=2\"$ . In other words, if 2 thousand autos are produced, then the cost will be at a minimum. Simply plug this value into the function to get:\r
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\n" ); document.write( "\n" ); document.write( " $\"C%282%29=4%282%29%5E2-16%282%29%2B32=4%284%29-16%282%29%2B32=16-32%2B32=16\"$ which means that $\"C%282%29=16\"$ . So the minimum cost is 16 million dollars (when 2 thousand autos are manufactured).\r
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\n" ); document.write( "\n" ); document.write( "So the vertex is the point (2,16). What this means is that if we graph $\"C%28x%29=+4x%5E2-16x%2B32\"$ , the lowest point on the graph is (2,16) \n" ); document.write( "

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