Suppose a rancher wants to fence off a rectangular shaped enclosure. He has 2400 feet of...

Suppose a rancher wants to fence off a rectangular shaped enclosure. He has 2400 feet of fencing that he can use. What are the dimensions that gives the enclosure the most area?

(a) Draw a sketch of the pen in this question. Appropriately label the relevant information in your sketch.

(b) Based on your sketch above, what equation is being maximized?

(c) Based on your sketch above, what equation represents the given constraint?

(d) Find the dimensions of the enclosure that gives the largest area.

(e) How much fence is used on the East-West sides? How much fence is used on the North-South sides? What is the ration of the amount of fence used on the East-West sides to the amount of fence used on the North-South sides?

Expert Solution

if satisfied with the explanation, please rate it up..

milcah answered 2 years ago

Next, let’s suppose a rancher wants to fence off a rectangular shaped enclosure that has two...

Next, let’s suppose a rancher wants to fence off a rectangular shaped enclosure that has two identical sections. You can think of this as a rectangle with an additional fence dividing the rectangle in half. For the sake of this question, he wants that additional fence running North-South (up-down). He still has 2400 feet of fencing that he can use. What are the dimensions that gives the enclosure the most area? (a) Use the sketch of the pen below for...

2. A rancher has set out to fence off a new rectangular pasture for her horses....

2. A rancher has set out to fence off a new rectangular pasture for her horses. She has 1000 feet of fencing to fence off as large an area as possible. She wants to give the horses some water access, so she is building the pasture along a river, which will not need fencing. (a) Write a function, P(x), that describes the area of the pasture as a function of its length, x. (Don’t need Python for this.) (b) Plot...

Texas rancher wants to fence off his four-sided plot of flat land. He measures the first...

Texas rancher wants to fence off his four-sided plot of flat land. He measures the first three sides, shown as A, B, and C in the figure below, where A = 4.15 km and ?C = 23°. He then correctly calculates the length in kilometers and orientation in degrees west of south of the fourth side D. What is his result in kilometers and degrees west of south? A= 4.15km corresponding degrees is 7.5 B= 2.48 and corresponding degrees is...

A farmer wants to fence in a rectangular pasture of 1.5 million square feet and then...

A farmer wants to fence in a rectangular pasture of 1.5 million square feet and then divide the pasture in half with a fence parallel to the sides of the rectangle. How can this be done in such a way as to minimize the amount of fencing required?

As a farmer, suppose you want to fence off a rectangular field that borders a river....

As a farmer, suppose you want to fence off a rectangular field that borders a river. You wish to find out the dimensions of the field that occupies the largest area, if you have 1200 feet of fencing. Remember that a square maximizes area, so use a square in your work. Draw several diagrams to express the situation and calculate the area for each configuration, then estimate the dimension of largest possible field. Find the function that models the area...

A farmer has 80 meters of fence to make an enclosure for his cows. The enclosure...

A farmer has 80 meters of fence to make an enclosure for his cows. The enclosure is divided into 2 sections by a fence parallel to one of the sides, as in the drawing below. One section is shaped like a half-hoop and the other is shaped rectangular. Find the dimensions that maximize the total area of the enclosure.

A rancher has 600 feet of fencing to enclose two adjacent rectangular corrals (see figure). (a)...

A rancher has 600 feet of fencing to enclose two adjacent rectangular corrals (see figure). (a) Write the area A of the corrals as a function of x. A(x) = (b) Construct a table showing possible values of and the corresponding areas of the corral. (Round your answers to two decimal places.) x A 55 60 65 70 75 80 Use the table to estimate the dimensions that will produce the maximum enclosed area. (Round your answers to two decimal...

A farmer has 1,700 feet of fence and wishes to build two identical rectangular enclosures, as...

A farmer has 1,700 feet of fence and wishes to build two identical rectangular enclosures, as in the following figure. What should be the dimensions of each enclosure if the total area is to be a maximum? What is the area of each enclosure?Answer with an exact fraction or round to the nearest whole number. Each enclosure will have width (shortest side) of feet, length (longest side) of feet and area of square feet.

Fencing a Farmer’s Field As a farmer, suppose you want to fence off a rectangular field that borders a river.

Fencing a Farmer’s Field As a farmer, suppose you want to fence off a rectangular field that borders a river. You wish to find out the dimensions of the field that occupies the largest area if you have 2000 feet of fencing. Remember that a square maximizes area, so use a square in your work. - Draw several diagrams to express the situation and calculate the area for each configuration, then estimate the dimension of the largest possible field. -...

Greg wants to build a rectangular enclosure for his animals. One side of the pen will...

Greg wants to build a rectangular enclosure for his animals. One side of the pen will be against the barn, so he needs no fence on that side. The other three sides will be enclosed with wire fencing. If Greg has 650 feet of fencing, you can find the dimensions that maximize the area of the enclosure. a) Let WW be the width of the enclosure (perpendicular to the barn) and let LL be the length of the enclosure (parallel...

Question