Question

In: Math

A farmer wants to fence in a rectangular plot of land adjacent to the north wall...

A farmer wants to fence in a rectangular plot of land adjacent to the north wall of his barn. No fencing is needed along the barn, and the fencing along the west side of the plot is shared with a neighbor who will split the cost of that portion of the fence. If the fencing costs $16 per linear foot to install and the farmer is not willing to spend more than $4000, find the dimensions for the plot that would enclose the most area.

(width, length) =

Solutions

Expert Solution



Related Solutions

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 builder wishes to fence in 72000 m 2 of land in a rectangular shape. For...
A builder wishes to fence in 72000 m 2 of land in a rectangular shape. For security reasons, the fence along the front part of the land will cost $ 25 per meter, while the fence for the other three sides will cost $ 11 per meter. How much of each type of fence should the builder buy to minimize the cost of the fence. What is the minimum cost? Use 4 decimal places for the fence amounts and round...
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 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.
ABC Daycare wants to build a fence to enclose a rectangular playground. The area of the...
ABC Daycare wants to build a fence to enclose a rectangular playground. The area of the playground is 920 square feet. The fence along three of the sides costs $5 per foot and the fence along the fourth side, which will be made of brick, costs $15 per foot. Find the length of the brick fence that will minimize the cost of enclosing the playground. (Round your answer to one decimal place.)
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. -...
A farmer, well versed in traditional optimization problems, has decided to buy a rectangular plot of...
A farmer, well versed in traditional optimization problems, has decided to buy a rectangular plot of 200 square meters of land on the bank of a river, and surround it on three sides by a fence. The side facing the river, will, of course, remain unfenced. What are the dimensions of the plot of land that can be surrounded by the minimum possible fencing?
You are a farmer and you are building a fence for your horses.  The fence will have...
You are a farmer and you are building a fence for your horses.  The fence will have four sides that are all the same.  The total budget for the project is $800 at $200 for each side.  The schedule for the project is 8 days (assume 8 hours per day), estimated at 2 days for each side.  The project started Monday morning and it is now Thursday (of the same week) at the end of the day ‘today’.  You assessed the progress and determined that...
A fence is to be built to enclose a rectangular area. The fence along three sides...
A fence is to be built to enclose a rectangular area. The fence along three sides is to be made of material that costs $5 per foot. The material for the fourth side costs $15 per foot.If $3,000 is available for the fencing, find the dimensions of the rectangle that will enclose the most area.
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT