What Is the Optimal Day to Sell Apples for Maximum Revenue?

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SUMMARY

The optimal day to sell apples for maximum revenue is determined by analyzing the revenue function R(t) = (-1/3)t^3 + 6t^2 + 16t + 10 and the loss function L(t) = 4t - 6. To maximize revenue, one must differentiate the revenue function with respect to time (t) and set the derivative equal to zero. The solution involves finding the critical points where the revenue is maximized, taking into account the rate of loss due to rot.

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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
 

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