document.write( "Question 413289: An orange growe has 400 crates of fruit ready for maret andwill have 20 more each day the grower waits. the present price is $60 per crate and will drop an estimated $2 per day for each day waited. In how many days should the grower ship the crop for maximum income? \n" ); document.write( "

Algebra.Com's Answer #290097 by ankor@dixie-net.com(22740) $\"\"$ $\"About$

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An orange growe has 400 crates of fruit ready for maret andwill have 20 more each day the grower waits.
\n" ); document.write( " the present price is $60 per crate and will drop an estimated $2 per day for each day waited.
\n" ); document.write( " In how many days should the grower ship the crop for maximum income?
\n" ); document.write( ":
\n" ); document.write( "Let x = no. of days to wait for max income
\n" ); document.write( ":
\n" ); document.write( "Income = no. of crates * price/crate
\n" ); document.write( "f(x) = (400 + 20x)*(60 - 2x)
\n" ); document.write( ":
\n" ); document.write( "FOIL
\n" ); document.write( "f(x) = 24000 - 800x + 1200x - 40x^2
\n" ); document.write( ":
\n" ); document.write( "Arrange as a quadratic equation
\n" ); document.write( "f(x) = -40x^2 + 400x + 24000
\n" ); document.write( ":
\n" ); document.write( "Max income occurs at the axis of symmetry, x = -b/(2a)
\n" ); document.write( "In this equation; a=-40; b= 400
\n" ); document.write( "x = $\"%28-400%29%2F%282%2A-40%29\"$
\n" ); document.write( "x = $\"%28-400%29%2F%28-80%29\"$
\n" ); document.write( "x = +5 days for max income \n" ); document.write( "

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