SOLUTION: 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

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?
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
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?
:
Let x = no. of days to wait for max income
:
Income = no. of crates * price/crate
f(x) = (400 + 20x)*(60 - 2x)
:
FOIL
f(x) = 24000 - 800x + 1200x - 40x^2
:
Arrange as a quadratic equation
f(x) = -40x^2 + 400x + 24000
:
Max income occurs at the axis of symmetry, x = -b/(2a)
In this equation; a=-40; b= 400
x =
x =
x = +5 days for max income
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