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?
:
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 = {{{(-400)/(2*-40)}}}
x = {{{(-400)/(-80)}}}
x = +5 days for max income