Finding the optimal harvest day to maximize apple revenue

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Homework Statement



Suppose it is the season for harvesting apples. You can earn (-1/3)
t^3 + 6t^2 + 16t + 10 GBP per kilo for the
apples you sell in good condition, where t denotes the number of days from the beginning of the harvest.
However you will lose apples to rot at the rate of 4t - 6 kg/day. On what day after harvest begins should
you sell your apples to maximise your revenue?


The Attempt at a Solution



It might just be because my head isn't working particularly well at the moment, but I can't see exactly what I need to differentiate and how the rate of change of value of apples relates to the rate of change of volume of apples.

Help appreciated :)
 
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11thHeaven said:

Homework Statement



Suppose it is the season for harvesting apples. You can earn (-1/3)
t^3 + 6t^2 + 16t + 10 GBP per kilo for the
apples you sell in good condition, where t denotes the number of days from the beginning of the harvest.
However you will lose apples to rot at the rate of 4t - 6 kg/day. On what day after harvest begins should
you sell your apples to maximise your revenue?


The Attempt at a Solution



It might just be because my head isn't working particularly well at the moment, but I can't see exactly what I need to differentiate and how the rate of change of value of apples relates to the rate of change of volume of apples.

Help appreciated :)

Suppose you sell the apples on day t. How many kg of apples do you sell? What is the selling price per kg for those sold apples?

RGV