document.write( "Question 809873: A car rental agency rents 200 cars per day at a rate of $30 per day. For each $1 increase in rate, 5 fewer cars are rented. At what rate should the cars be rented to produce a maximum income? What is the maximum income? \n" ); document.write( "

Algebra.Com's Answer #487867 by josgarithmetic(39617) $\"\"$ $\"About$

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Starting income, $\"200%2A30\"$ dollars per day.
\n" ); document.write( "The 1 dollar rate per day increase (price) does this:
\n" ); document.write( " $\"%28200-5%2Ax%29%2830%2Bx%29\"$ for the income per day.\r
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\n" ); document.write( "\n" ); document.write( "Not given if that income is revenue or profit, so it might simply be called, y:
\n" ); document.write( " $\"highlight%28y=%28200-5x%29%2830%2Bx%29%29\"$ , and we might expect x to be whole numbers, although might not need such a restriction. \r
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\n" ); document.write( "\n" ); document.write( "The equation is quadratic and has a maximum, which is what we are asked to find. \r
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\n" ); document.write( "\n" ); document.write( "Consider the zeros of y. They occur at x=40 and x=-30. Do not worry about any $\"x%3C0\"$ , because they would not be actual values of x; they would be hypothetical only. We want the x value exactly in the middle of 40 and -30.\r
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\n" ); document.write( "\n" ); document.write( "Max x is at $\"%2840%2B%28-30%29%29%2F2=10%2F2=highlight%285%29\"$ .
\n" ); document.write( "This means that the rental rate should be $\"30%2B5=highlight%2835%29\"$ dollars. \n" ); document.write( "

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