The annual yield per walnut tree is fairly constant at 60 pounds per tree when the number of trees per acre is 20 or fewer. For each additional tree over 20, the annual yield per tree for all trees on the acre decreases by 2 pounds due to overcrowding. Find the annual yield of walnuts on the acre as a function of the number of walnut trees. (Assume that the number of walnut trees per acre is greater than 20.)

Question

The annual yield per walnut tree is fairly constant at 60 pounds per tree when the number of trees per acre is 20 or fewer. For each additional tree over 20, the annual yield per tree for all trees on the acre decreases by 2 pounds due to overcrowding. Find the annual yield of walnuts on the acre as a function of the number of walnut trees. (Assume that the number of walnut trees per acre is greater than 20.)

Answer 1

so, if there are x trees over 20, then the yield per tree is 60-2x

The total ranch yield is thus y = (20+x)(60-2x)

Answer 2

sorry -- not total ranch yield -- just the total yield per acre.

Answer 3

Let's break down the problem step-by-step:

Step 1: Define the variables:
Let's denote:
- x as the number of walnut trees on the acre.
- y as the annual yield of walnuts on the acre.

Step 2: Determine the base yield:
According to the problem, when the number of trees per acre is 20 or fewer, the annual yield per tree is a constant 60 pounds. So, for x ≤ 20, the base yield is 60x pounds.

Step 3: Determine the decrease in yield:
For each additional tree over 20, the yield per tree for all trees on the acre decreases by 2 pounds due to overcrowding. So, for trees beyond 20, the decrease in yield is 2(x - 20) pounds.

Step 4: Calculate the total yield:
The total yield is the base yield minus the decrease in yield. Therefore, the annual yield of walnuts on the acre can be expressed as:

y = 60x - 2(x - 20)

Step 5: Simplify the equation:
y = 60x - 2x + 40

Simplifying further, we get:

y = 58x + 40

So, the annual yield of walnuts on the acre is given by the function y = 58x + 40, where x is the number of walnut trees on the acre.

Answer 4

To find the annual yield of walnuts on the acre as a function of the number of walnut trees, we can break down the problem into two parts:

1. Determine the annual yield per tree based on the number of trees per acre.
2. Calculate the total annual yield for all the trees on the acre.

Let's start with the first part:

1. Determine the annual yield per tree based on the number of trees per acre.

When there are 20 or fewer trees per acre, the annual yield per tree is a constant 60 pounds.

For each additional tree over 20, the annual yield per tree decreases by 2 pounds due to overcrowding.

So, if "x" represents the number of trees over 20, then the annual yield per tree for all trees on the acre can be calculated as:

Annual yield per tree = 60 - (2 * x)

Now, let's move on to the second part:

2. Calculate the total annual yield for all the trees on the acre.

To calculate the total annual yield, we need to multiply the annual yield per tree by the total number of trees on the acre.

Let's say "n" represents the total number of walnut trees on the acre. Since we have "x" trees over 20, the number of trees per acre would be (20 + x).

Therefore, the total annual yield for all the trees on the acre can be calculated as:

Total annual yield = (60 - (2 * x)) * (20 + x)

This equation represents the annual yield of walnuts on the acre as a function of the number of walnut trees.