document.write( "Question 71252: A manufacturer of lighting fixtures has daily production costs modeled by y=0.25x^2-10x+800 where y is the total cost in dollars and x is the number of fixtures produced\r
\n" ); document.write( "\n" ); document.write( "How many fixtures should be produced each day to yield a minimum cost? \n" ); document.write( "

Algebra.Com's Answer #50981 by Earlsdon(6294) $\"\"$ $\"About$

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The total cost is given by:
\n" ); document.write( " $\"y+=+0.25x%5E2-10x%2B800\"$
\n" ); document.write( "Find the value of x that will give the minimum y.
\n" ); document.write( "Notice that the equation is that of a parabola that opens upward. So if you can find the vertex of this parabola, you will have found the minimum.
\n" ); document.write( "The x-coordinate of the vertex of a parabola can be found by:
\n" ); document.write( " $\"x+=+%28-b%29%2F2a\"$ where the a and b come from: $\"ax%5E2%2Bbx%2Bc=0\"$ the general form for the quadratic equation.
\n" ); document.write( "In your problem, a = 0.25 and b = -10
\n" ); document.write( " $\"x+=+%28-%28-10%29%29%2F2%280.25%29\"$ Simplify.
\n" ); document.write( " $\"x+=+10%2F0.5\"$
\n" ); document.write( " $\"x+=+20\"$
\n" ); document.write( "So 20 fixtures should be produced each day to yield a minimum cost.
\n" ); document.write( "If you wanted to find this minimum cost, you would simply substitute x=20 into the original equation and solve for y. \n" ); document.write( "

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