Suppose a rectangular pasture is to be constructed using 1 2 linear mile of fencing. The pasture will have one divider parallel to one pair of sides and two dividers parallel to the other pair of sides, so that there are six congruent enclosures. What is the maximum total area of such a pasture, in square feet?

Step-by-step explanation:

Maximization With Derivatives

Given a function of one variable A(x), we can find the maximum or minimum value of A by using the derivatives criterion. If A'(x)=0, then A has a probable maximum or minimum value.

We need to find a function for the area of the pasture. Let's assume the dimensions of the pasture are x and y, and one divider goes parallel to the sides named y, and two dividers go parallel to x.

The two divisions parallel to x have lengths y, thus the fencing will take 4x. The three dividers parallel to y have lengths x, thus the fencing will take 3y.

The amount of fence needed to enclose the external and the internal divisions is

We know the total fencing is 1/2 miles long, thus

Solving for x

The total area of the pasture is

Substituting x

Differentiating with respect to y

Equate to 0

Solving for y

And also

Compute the second derivative

Since it's always negative, the point is a maximum

Thus, the maximum area is

pakistan's principal natural resources are arable land and water. about 25% of pakistan's agriculture accounts for about 21% [1] of gdp and employs about 43% of the labour force. in pakistan, the most agricultural province is punjab where wheat and cotton are the most grown.

you would need to also lose 1 point for each of the other outcomes for it to be fair.

step-by-step explanation: