How much fencing is needed for a rectangular garden 93 feet by 63 feet

In a single growing season at the smith family orchard, the average yield per apple tree is 150 apples when the number of trees

Mariana [72]

Answer:

100 trees should be planted per acre to maximize the total yield (15000 apples per acre)

Step-by-step explanation:

<u>Functions </u>

Expressing some quantities in terms of other(s) comes in handy to understand the behavior of the situations often modeled by those functions.

Our problem tells us about the smith family orchard, where the average yield per apple tree is 150 apples when the number of trees per acre is 100 (or less). But the average yield per tree decreases when more than 100 trees are planted. The rate of decrease is 1 for each additional tree is planted

Let's call x the number of trees planted per acre in a single growing season. We have two conditions when modeling: when x is less than 100, the average yield per apple tree (Ay) is (fixed) 150.

$Ay(x)=150\ ,\ x\leqslant 100$

When x is more than 100:

$Ay(x)=150-x\ ,\ 100< x\leqslant 150$

The upper limit is 150 because it would mean the Average yield is zero and no apples are to be harvested

Part 1

We are asked what happens if the number of trees per acre was doubled, but we don't know what the original number was. Let's make it x=60

If x=60, then we must use the first function, and

Ay(60)=150

The yield per acre will be 150*60=9000 apples

If we doubled x to 120, we would have to use the second function

Ay(120)=150-x=30

The yield per acre will be 30*120=3600 apples

Note that doubling the number of trees would make the production decrease

If we started with x=30, then

Ay(30)=150, and we would have 150*30=4500 apples per acre

We already know that for x=60 (the double of 30), our production will be 9000 apples per acre

This shows us that in some cases, increasing the number of trees is beneficial and in other cases, it is not

Part 2

The total yield is computed as

Y(x)=x.Ay(x)

This function will be different depending on the value of x

$Y(x)=150x\ ,\ x\leqslant 100$

$Y(x)=150x-x^2\ ,\ 100< x\leqslant 150$

To find the maximum total yield we take the first derivative

$Y'(x)=150\ ,\ x\leqslant 100$

$Y'(x)=150-2x\ ,\ 100< x\leqslant 150$

The first expression has no variable, so the total yield must be evaluated in the endpoints

Y(0)=0

Y(100)=15000

Now, the second expression contains variable, it will be set to 0 to find the critical point

150-2x=0

x=75

x is outside of the boundaries, we cannot find the maximum in this interval

Answer: 100 trees should be planted per acre to maximize the total yield (15000 apples per acre)

7 0

4 years ago

If each cube has a side measure of 12 inch, what is the volume of the rectangular prism?

barxatty [35]

Answer:

nii pata didi plz dil dedo

5 0

3 years ago

Read 2 more answers

As part of a chemistry experiment, Barry is making a mixture of two solutions. He uses 4 cups of solution A for every 2 cups of

sergejj [24]

Answer:

A. The ratio of the number of cups of solution A to the total number of cups of the mixture is 2:3

Step-by-step explanation:

Solution A= 4 cups

Solution B= 2 cups

Total cups of the mixture=4+2=6

A. The ratio of the number of cups of solution A to the total number of cups of the mixture is 2:3.

Solution A= 4 cups

Mixture=6 cups

Solution A : Mixture =4 : 6

=2:3

Option A is true

B. The ratio of the number of cups of solution A to the total number of cups of the mixture is 3:2.

Solution A= 4 cups

Mixture=6 cups

Solution A : Mixture =4 : 6

=2:3

Option B not true

C. There are 3 cups of solution A for every 6 cups of mixture.

Option C states that:

Solution A=3 cups

Mixture=6 cups

Solution A : Mixture=3:6=1:2

This is not true

D. For each cup of solution A, there are 2 cups of solution B.

Option D states:

Solution A= 1 cups

Solution B= 2 cups

This is not true

It is rather

Solution A= 2 cups

Solution B= 1 cups

Therefore, option A. The ratio of the number of cups of solution A to the total number of cups of the mixture is 2:3 is the correct statement

5 0

3 years ago

How do you find the perimeter on a coordinate plane

hoa [83]

Answer: You draw the shape on the coordinate plan and then you can count the number of unit squares

Step-by-step explanation:

4 0

1 year ago

(1/8)b -9 = -4. could anyone please help me out I'm having trouble

Naya [18.7K]

Answer:

40

Step-by-step explanation:

(1/8)b = 5

b = 5 : 1/8

b = 40

5 0

3 years ago