document.write( "Question 824302: How do i solve the following equation? A company producing steel construction bars uses the function R(x) = -0.04x2+6.8x -100 to model the unit revenue in dollars for producing x bars. For what number of bars is the revenue at a maximum? What is the unit revenue at that level of production? \n" ); document.write( "

Algebra.Com's Answer #496263 by fcabanski(1391) $\"\"$ $\"About$

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Take the derivative and set it = to 0 to find the max.

\n" ); document.write( "Derivative of $\"+-0.04x%5E2%2B6.8x+-100\"$ = -.08x + 6.8 = 0

\n" ); document.write( "-.08x = -6.8

\n" ); document.write( "x = 85

\n" ); document.write( "Verify it's a max by looking at the value of the derivative for the interval -inf to 85 and 85 to inf. If 85 is a max, the derivative will be positive before 85 and negative after 85.

\n" ); document.write( "0 is in the first interval: -.08*0 + 6.8 is positive.

\n" ); document.write( "100 is in the second interval: -.08*100 + 6.8 = -8 + 6.8 is negative.

\n" ); document.write( "The graph is rising before x=85 and falling after x=85, so 85 is a maximum.
\n" ); document.write( "Plug 85 into the equation to find the unit revenue.

\n" ); document.write( " $\"+-0.04%2A%2885%5E2%29%2B6.8%2885%29+-100+=+189\"$ \n" ); document.write( "

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