2. A farmer plans to fence a rectangular pasture adjacent to a river. The pasture must contain 245,000 square meters in order to provide enough grass for the herd. What dimensions will require the least amount of fencing if no fencing is needed along the river?

Q: 15. You want to put a fence around a rectangular field and then subdivide the field into 4 smaller…

A: Let's find.

Q: If the farmer has 162 feet of fencing, what are the dimensions of the region which enclose the…

A: Let dimesnion of the region is x and ysince, the farmer has 162 feet of fencingtherefore,…

Q: (a) The service elevator at AR Hector Financial Complex has a maximum capacity of 2870 lbs. If the…

A: Note: There are three different question, so we are doing only first question.   Maximum capacity of…

Q: A worker is to construct an open rectangular box with the square base and volume of 12 ft.³. If…

A:

Q: 12. Show that a rectangle with given perimeter has maximum area when it is a square.

A:

Q: Three equally sized rectangular lots are enclosed by fencing the perimeter of a large rectangular…

A: Figure Three equally sized rectangular

Q: 1.4 Optimize Perimeter and Area 10. A soccer coach is fencing in a rectangular area of the playing…

A:

Q: 9. The management of a large store wishes to add a fenced-in rectangular storage yard of 20,000…

A:

Q: 5. Find the length and width of a rectangle that has an area of 32 square feet and a minimum…

A: Given, area A=32 sq.ft Let, x be the length and y be the width. The formula for the area of a…

Q: 2. Suppose an airline policy states that all baggage must be rectangle-shaped with the sum of the…

A: We first calculate the side of square box then calculate its volume. Using formula Volume of cube…

Q: A rectangular prism has a height of 11.5 inches, a length of 9.6 inches, and a width of 2.10 inches.…

A:

Q: 5. A farmer wants to fence an area of 9600 square feet in a rectangular field and then divide it in…

A:

Q: A worker is to construct an open rectangular box with a square base and a volume of 128 ft. If…

A:

Q: Suppose an airline policy states that all baggage must be​ box-shaped with a sum of​ length, width,…

A: Modelling the problem: Let the three dimension be x, x and y .Since base is a square base.   also…

Q: A box with a square base and an open-top is to be constructed. The base will be made of material…

A:

Q: A contractor has to build rectangular pool 12 meters long and 8 meters wide. The pool must, by…

A: Given: Length of pool = 12 meter Breadth of pool = 8 meter  The area of rectangular border must be…

Q: A window is being built and the bottom is a rectangle and the top is a semicircle. If there is 12…

A:

Q: what is the minimum possoble perimeter for a rectangle whose area is 100 in^2

A:

Q: A farmer wants to construct a fence around an area of 726 square feet in a rectangular field and…

A: Dimensions:  33×22

Q: (c) A contractor has to build rectangular pool 12 metres long and 8 metres wide. The pool must, by…

A: (i) It is given that the length of the rectangular pool is 12 m and width is 8 m and the area is 12…

Q: A rectangular plot of farmland will be bounded on one side by a river and on the other three sides…

A: Given  Total length of the fence=2500 m Letl=length of the plotb=width of the plot

Q: 12. The sum of the perimeters of an equilateral triangle and a square is 10. Find the dimensions of…

A: Given: The objective is to find the dimensions of square and an equilateral triangle whose perimeter…

Q: The maximum possible volume of a rectangular box with the sum of its twelve edges 60 cm is

A: Given 12 edges sum is 60, let C=60So, 4x+4y+4z=CV=xyz    =xy(14C-x-y)    =14Cxy-x2y-xy2 for x>0,…

Q: 1. A farmer wants to fence in a field and divide it into four side by side, equal areas. If he wants…

A: From the given data And, xy=8000&f(x,y)=2x+5y is the parimeter to minimize.

Q: A farmer wants to construct a fence around an area of 6936 square feet in a rectangular field and…

A:

Q: Suppose the farmer makes the rectangular holding pen using an existing fence for one side. What…

A: Let the farmer makes the rectangular holding pen using an existing fence for one side.  let the…

Q: A rancher plans to make four identical and adjacent rectan- gular pens against a barn, each with an…

A: Let the width of each pen be x and the length of each pen be y. As the pens are rectangular thus the…

Q: Suppose an airline policy states that all baggage must be box-shaped with a sum of length, width,…

A: We will use second derivative test to find the maximum volume.

Q: 1. The minimum possible perimeter for a rectangle with an area of 529 m² is

A: Note:- Since you have asked multiple question As per our policy, we will solve the first question…

Q: A builder must fence all sides of 3 adjacent rectangular lots, each having 168 m2 of area. Front…

A:

Q: A farmer wishers to fence off three identical adjoining rectangular pens, each with 300 square feet…

A: Given, Cost of the fence of outer boundary of the pens = $3 per foot Cost of the fence of two…

Q: A wire b is cut into two pieces. One piece is bent into an equilateral triangle and the other is…

A:

Q: 2. Find the length and width of a rectangle that has an area of 64 square feet and a minimum…

A: Find the length and width of the rectangle

Q: 19. If the farmer in Exercise 18 wants to enclose 150 square meters of land, what dimensions will…

A: The minimum of a function can be obtained at the point where the slope of the function is 0. The…

Q: 4. A television manufacturing firm needs to design an open-topped box with a square base. The box…

A: Here we have to follow the steps according to the question information to get the answer so I'm…

Q: A farmer wants to start raising cows, horses, goats, and sheep and desires to have a rectangular…

A: We have to find maximum possible area that each of the four pens will enclose.

Q: 8. US Postal Service regulations state that the length plus the girth of a package cannot exceed 108…

A: Take length of box = y width = height = x girth = 2*width +2*height         = 2x+ 2x          = 4x

Q: A farmer needs to enclose a rectangular pasture containing 2,500,000 square feet. Suppose that along…

A: Given that area=2,500,000 square feet So, xy=2500000  Or, y=2500000/x   Total cost: C=15x+10y+10x or…

Q: ndscape architect wished to enclose a rectangular garden on one side by a brick wall costing $40/ft…

A:

Q: A farmer wants to construct a fence around an area of 7776 square feet in a rectangular field and…

A:

Q: 5., You are building TWO identical pens adjacent to each other with a total area of 100 m², as shown…

A: Let's solve 5th question, dimensions for minimize the amount of fencing.

Q: A gardener wants to construct 4 garden areas by first building a fence around a rectangular region,…

A:

Q: 2. Find the dimensions of a rectangle with an area of 108 square feet that has the minimum…

A: Area of rectangle = (length)*(width) = 108 sq. ft we need to find dimensions of a rectangle with…

Q: A rectangular plot of farmland will be bounded on one side by a river and on the other three sides…

A: Let a and b be the sides of a retangular fence.

Q: If a cube has edges that are each three times as long as a second cube, then its volume will be nine…

A: Volumes

Q: A landscape architect wished to enclose a rectangular garden on one side by a brick wall costing…

A:

Q: 5. A rectangular plot of farmland will be bounded on one side by a river and on the other three…

A: Given length of the wire, L=800 m Let the length of the rectangular area=x  Width of the rectangular…

Q: 2. b. A farmer wants to fence an area of 1.5 million square feet in a rectangular field and then…

A: Given: Fence area =1.5 million square feet

Q: Suppose an airline policy states that all baggage must be rectangular with a sum of length, width,…

A:

Q: (c) A contractor has to build rectangular pool 12 metres long and 8 metres wide. The pool must, by…

A: (i) Let x be the width of the border. Given that, the rectangular pool is 12 meters long and 8…