A strawberry farmer will receive $4 perbushel of strawberries if the strawberries are harvested this week.Each week that passes, the value drops by $0.10 per bushel. Thefarmer estimates that there are approximately 120 bushels ofstrawberries in the fields, and that the crop is increasing at arate of 4 bushels per week. 1. write a function R that gives the expected revenue from thestawberry harvest as a function of n, the number of weeks that thefarmer waits to harvest. 2. when should the farmer harvest the strawberries to maximize therevenue from the harvest? 3. how many bushels of strawberries will yield the maximum possiblerevenue? What is the maximum revenue?

podmitijuy0

podmitijuy0

Answered question

2022-08-04

A strawberry farmer will receive $4 perbushel of strawberries if the strawberries are harvested this week.Each week that passes, the value drops by $0.10 per bushel. Thefarmer estimates that there are approximately 120 bushels ofstrawberries in the fields, and that the crop is increasing at arate of 4 bushels per week.
1. write a function R that gives the expected revenue from thestawberry harvest as a function of n, the number of weeks that thefarmer waits to harvest.
2. when should the farmer harvest the strawberries to maximize therevenue from the harvest?
3. how many bushels of strawberries will yield the maximum possiblerevenue? What is the maximum revenue?

Answer & Explanation

Zechariah Zavala

Zechariah Zavala

Beginner2022-08-05Added 14 answers

From the given information, we can write the price of a single bushel of strawberries as a functiondependent on the variable n (weeks) .
The price declines by $0.10 every month from astarting priceof $4.
i.e Price of single bushel after n weeks , b(n)=4-(0.1)n
Similarly,The production of bushels is a dependent function ofn.
After n weeks the Total number of bushels will beB(n)=120+4n
1. The expected Revenue(R) in nth week is given by theproduct of b(n) and B(n).
R ( n ) = b ( n ) B ( n ) = ( 120 + 4 n ) ( 4 ( 0.1 ) n )
2.To maximize the revenue:
we use the method of maxima and minima to findthe n for which The revenue will be maximum.
i.e we solve d R d n = 0 4 ( 4 / 5 ) n = 0 n=5weeks
and also d d n d d n ( R ) = ( 4 / 5 ) < 0 which confirms that the critical point n=5 corresponds to the maximum Revenue
The former should harvest the strawberries justafter 5 weeks of time.
3.The number of bushels after 5 weeks will be B(5)=140 whichcorresponds to the max possible yield.
And the Max Revenue is R(5)=$490

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?