A farmer finds that if she plants 70 trees per acre, each tree will yield 75 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?

Question

northjerseypi4240 northjerseypi4240

10-08-2019
Mathematics

contestada

A farmer finds that if she plants 70 trees per acre, each tree will yield 75 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?

Respuesta :

Otras preguntas

Speakeasies were places where what was sold illegally? Musical instruments Stolen goods Alcohol Guns

how important was international trade to Britain's economic development in the 19th century?

At first a price was decreased by 12%, then it was discounted again by an additional 5%. What is the percent of the total discount? Its not 17%

Exercise 2.7 a car is stopped at a traffic light. it then travels along a straight road so that its distance from the light is given by x(t)=bt2−ct3, where b =

In 1846 semmelweis has his physicians to clean their hand in a____ solution before delivering a baby which reduced the morality rate of mother's from 7% to 1%

There are four different routes that Cassidy can walk from home to the post office and two different routes that she can walk from the post office to the bank.

You are helping the school nurse decide which students are most at risk for health problems. Look at these four cases. Which person seems most likely to abuse

Can share electrons in single pairs, double pairs, or triple pairs. share electrons in triple pairs. share electrons in single pairs. share electrons singly, ne

find the area of the figure A- 50ft squared B- 41ft squared C- 42ft squared D- 38ft squared

A person who is 6 feet tall has a 2 foot shadow, while a telephone pole has a 16 foot long shadow. How tall is the telephone pole?

sqdancefan sqdancefan · Answer 1 · 2019-08-10T10:39:57+02:00

Answer:

44 3/8 trees per acre

Step-by-step explanation:

Let x represent the number of trees planted per acre. Let y represent the yield in bushels per tree. The farmer estimates the yield will be ...

y = 75 -4(x -70)

y = 355 -4x . . . . . . simplify

The yield per acre is this yield per tree multiplied by the number of trees per acre, x.

yield per acre = x(355 -4x) = 4(x)(88.75 -x)

This describes a downward-opening parabola with zeros at x=0 and x=88.75. The vertex (maximum) is halfway between the zeros, at x = 44.375.

To maximize her harvest, the farmer should plant 44 3/8 trees per acre. If the model is correct, each tree would then produce 177.5 bushels of fruit, almost 2.4 times the current yield.