A certain area of forest is populated by two species of animal, which scientists refer to as A and B for simplicity. The forest supplies two kinds of food, referred to as

and
For one year, each member of species A requires 1 unit of
and 0.5 unit of
. Each member of species B requires 0.2 unit of
and 1 unit of
. The forest can normally supply at most 600 units of
and 525 units of
per year. What is the maximum total number of these animals that the forest can support?

You need to proofread your post; the copy/paste of teh food type names did not work.

So, you know that
1.0A + 0.2B <= 600
0.5A + 1.0B <= 525
and you want to maximize p = A+B
so graph the region and evalueate p(A,B) at the vertices.

It would help if you would proofread your work before you post it.

Units of what?

To determine the maximum total number of animals that the forest can support, we need to calculate the resource requirements for both species A and B and then compare it to the available resources.

First, let's calculate the resource requirements for species A for one year:

- Each member of species A requires 1 unit of and 0.5 unit of .
- Let's assume there are 'x' members of species A in the forest.
- The total resource requirement for species A in a year would be: x * (1 unit of ) + x * (0.5 unit of ).

Next, let's calculate the resource requirements for species B for one year:

- Each member of species B requires 0.2 unit of and 1 unit of .
- Let's assume there are 'y' members of species B in the forest.
- The total resource requirement for species B in a year would be: y * (0.2 unit of ) + y * (1 unit of ).

Now, let's compare the resource requirements to the available resources:

- The forest can supply at most 600 units of per year, which means the total resource requirement for should be less than or equal to 600.
- The forest can supply at most 525 units of per year, which means the total resource requirement for should be less than or equal to 525.

Combining these inequalities, we can write the following equations:

x + 0.2y <= 600 (equation 1)
0.5x + y <= 525 (equation 2)

To find the maximum total number of animals, we need to find the maximum values of x and y that satisfy these inequalities.

To solve these equations, we can use the method of substitution or elimination. Here, we will use the method of elimination.

Multiply equation 1 by 5 to eliminate x:

5x + y <= 3000 (equation 3)

Now, subtract equation 2 from equation 3:

(5x + y) - (0.5x + y) <= 3000 - 525
4.5x <= 2475
x <= 550

Substituting this value of x into equation 2:

0.5 * 550 + y <= 525
y <= 525 - 275
y <= 250

Therefore, the maximum total number of animals the forest can support is 550 individuals of species A and 250 individuals of species B.

To find the maximum total number of animals that the forest can support, we need to consider the availability of both kinds of food and the food requirements of both species.

Let's start by calculating the maximum number of animals that can be supported based on the availability of each kind of food:

- For food _, the maximum number of animals that can be supported is 600 units / 1 unit per species A = 600 species A.

- For food _, the maximum number of animals that can be supported is 525 units / 0.2 units per species B = 2625 species B.

Now, we need to compare the food requirements of each species to determine the limiting factor.

For species A:
- Each member of species A requires 1 unit of _ and 0.5 unit of _.

For species B:
- Each member of species B requires 0.2 unit of _ and 1 unit of _.

To determine the limiting factor, we need to find out how many animals of each species can be supported based on these requirements.

Let's calculate the number of species A that can be supported based on the availability of each kind of food:

- For _, the number of species A that can be supported is 600 units / 1 unit per species A = 600 species A.

- For _, the number of species A that can be supported is 525 units / 0.5 units per species A = 1050 species A.

Therefore, the maximum number of species A that can be supported is 600 species A.

Next, let's calculate the number of species B that can be supported based on the availability of each kind of food:

- For _, the number of species B that can be supported is 600 units / 0.2 units per species B = 3000 species B.

- For _, the number of species B that can be supported is 525 units / 1 unit per species B = 525 species B.

Therefore, the maximum number of species B that can be supported is 525 species B.

Now, we need to determine the minimum value between the maximum number of species A and the maximum number of species B, as that will be the limiting factor.

The minimum value is 525 (the maximum number of species B).

Therefore, the maximum total number of animals that the forest can support is 525 species A + 525 species B = 1050 animals in total.