document.write( "Question 106117: a manufacturer finds that the total cost C for a product is expressed by C=250x^2 - 24,000, and the total revenue R at a price of 200 per unit to be R=200x - 1,000, where x is the number of units sold. what is the break-even point (where total cost = total revenue) to the nearest unit? \n" ); document.write( "

Algebra.Com's Answer #77201 by Fombitz(32388) $\"\"$ $\"About$

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$\"C=250x%5E2+-+24000\"$
\n" ); document.write( " $\"R=200x+-+1000\"$
\n" ); document.write( "Find x when C=R?
\n" ); document.write( " $\"C=R\"$
\n" ); document.write( " $\"250x%5E2-24000=200x-1000\"$
\n" ); document.write( " $\"250x%5E2-200x-23000=0\"$
\n" ); document.write( "Use the quadratic formula,
\n" ); document.write( " $\"x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+\"$
\n" ); document.write( "

\n" ); document.write( " $\"x+=+%28200+%2B-+sqrt%28+23040000+%29%29%2F%28500%29+\"$
\n" ); document.write( " $\"x+=+%28200+%2B-+%284800%29%29%2F%28500%29+\"$
\n" ); document.write( "Since a negative unit sold doesn't make sense, we'll only calculate the positive value.
\n" ); document.write( " $\"x+=+%285000%29%2F%28500%29+\"$
\n" ); document.write( " $\"x+=+10+\"$
\n" ); document.write( "10 units is the break-even point. \n" ); document.write( "

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