Farmer wants to build a rectangular corral next to a straight river with the river serving as one side of the corral. If the farmer has only 40 40 m of fencing with which to build the corral, what dimensions will maximize its area? Express the area A ( w ) A ( w ) of the corral as a function of its width w w .

Dimensions of the rectangular corral will be 20m × 10m.

Step-by-step explanation:

Farmer wants to build a rectangular corral next to a straight river.

So, to build a coral farmer will use the fence on three sides only (excluding river side).

Let length of the rectangular corral = l m

and width of the corral = w m

Area of the corral A = lw  ------(1)

Since length of the fence that the farmer has = 40 m

So, 40 = l + w + w

l + 2w = 40

l = 40 - 2w -----(2)

Now we substitute the value of w in equation (1)

We can write the area in the form of the function as

For maximum area we will find the derivative of the area and equate it to zero.

A'(w) = 0

40 - 4w = 0

w = 10 m

From equation (2),

l = 40 - 2(10)

l = 20 m

Therefore, dimensions of the rectangular corral will be 20m × 10m

87%

step-by-step explanation:

apex answer