SOLUTION: A farmer finds that if she plants 80 trees per acre, each tree will yield 65 bushels of fruit. She estimates that for each additional tree planted per acre, the yield of each tree

Question 1087310: A farmer finds that if she plants 80 trees per acre, each tree will yield 65 bushels of fruit. She estimates that for each additional tree planted per acre, the yield of each tree will decrease by 4 bushels. How many trees should she plant per acre to maximize her harvest?
Answer by ikleyn(52800) (Show Source): You can put this solution on YOUR website!
.
This problem, considered as it is stated, makes no sense.

Below I presented the plot of the quadratic function for the total harvest as function of the number of trees per acre.

This quadratic function was built formally based on the given condition
(extrapolated for x >= 80 and for x <= 80, where x is the number of trees per acre).

The maximum is at x ~ = 48.125,
but the condition says NOTHING about the behavior of this function when n (or x) decreases below 80.

Therefore I state that the problem (given as it is formulated) makes no sense.

Plot y =

For solution of similar problem (but correctly formulated !!!) see the link

https://www.algebra.com/algebra/homework/Finance/Finance.faq.question.1078355.html

https://www.algebra.com/algebra/homework/Finance/Finance.faq.question.1078355.html

in this forum.

RELATED QUESTIONS
A farmer finds that if she plants 95 trees per acre, each tree will yield 30 bushels of... (answered by greenestamps)

An orange grower finds that she gets a yield of 40 bushels of oranges per tree when she... (answered by stanbon)

An orange grower finds that she gets an average yield of 40 bushels per tree when she... (answered by josmiceli)

The owner of the local apple orchard estimates that if 24 trees are planted per acre,... (answered by ikleyn,Theo)

PLEASE HELP ME WITH THIS PROBLEM< ITS MY LAST ONE AND I'M STUCK!!!! ***I NEED THE... (answered by ankor@dixie-net.com)

In a 6 acre apple orchard, it is decided to plant 20 or more trees per acre. If 20 trees... (answered by Theo)

1.) A citrus grower estimates that if 60 orange trees are planted, the average yield per... (answered by KMST)

Each orange tree grown in California produces 630 oranges per year if not more than 20... (answered by ikleyn)