(a) A rancher wants to enclose a rectangular part of a large pasture so that 1 000 km 2 is enclosed with the minimum amount of fence Find the dimensions of the rectangle that he should choose The area is A xy but A is fixed at 1 000 km 2 , so that y A x (b) The rancher now decides that the fenced area must lie along a road and finds that the fence costs $20 00 per meter along the road and $10 00 per meter along the other edges Find the dimensions of the rectangle that would minimize the cost of the fence

Question: (a) A rancher wants to enclose a rectangular part of a large pasture so that 1.000 km 2 is enclosed with the minimum amount of

(a) A rancher wants to enclose a rectangular part of a large pasture so that 1.000 km² is enclosed with the minimum amount of fence. Find the dimensions of the rectangle that he should choose. The area is

A = xy

but A is fixed at 1.000 km², so that y = A/x.

(b) The rancher now decides that the fenced area must lie along a road and finds that the fence costs $20.00 per meter along the road and $10.00 per meter along the other edges. Find the dimensions of the rectangle that would minimize the cost of the fence.

Step by Step Solution

★★★★★

3.49 Rating (169 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

a The perimeter of the area is p 2x 2y 2x 2... View full answer

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Students Have Also Explored These Related Mathematics Physical Chemistry Questions!

What's this story about? A Lot of Weeding Masa walked slowly toward the house, stopping now and then to snip off fading flowers, or to pull out weeds growing between the plants. But there were very...

A farmer with 4000 meters of fencing wants to enclose a rectangular plot that borders on a river. If the farmer does not fence the side along the river, what is the largest area that can be enclosed?...

A farmer with 10,000 meters of fencing wants to enclose a rectangular field and then divide it into two plots with a fence parallel to one of the sides. See the figure.What is the largest area that...

A rectangular area is to be enclosed and divided into thirds. The family has $800 to spend for the fencing material. The outside fence costs $10 per running foot installed, and the dividers cost $20...

prompt help Ifyou have 300 meters of fencing and want to enclose a rectangular area up against a long, straight wall, what is the largest area you can enclose? Area = 1" (include units) HINTS: Keep...

3.1 Higher Order Derivatives. Velocity and Acceleration 1 . Find f' , f" , f " , f ( 4) , f (5) , f () for f ( x ) = x5 + x3 - x2 + x+ 2. 2. Find f' and f" for f(x) =V1-x2 . Write the answers in a...

3.1 Higher Order Derivatives. Velocity and Acceleration 1 . Find f' , f" , f" , f ( 4 ) , f (5 ) , f ( 6 ) for f ( x ) = x5 + x 3 - x 2 + x + 2 . 2. Find f' and f" for f(x) = V1-x2 . Write the...

3.3 Optimization Problems 5. A farmer with 800m of fencing wants to enclose a rectangular area and then divide it into five pens (of equal size) with fencing parallel to one side of the rectangle...

1. Centerville is the headquarters of Greedy Cablevision inc. The cable company is about to expand service to two nearby towns, Springfield and Shelbyville. There needs to be cable connecting...

the following question in topic of calculus and vector I have ask question similiar before too so if you knowing, this same person. hello, I cannot answer these because I have family emergency back...

Please help solve the following problems: 1. A farmer with 750 ft of fencing wants to enclose a rectangular area and then divide it into four pens with fencing parallel to one side of the rectangle....

Take the derivative to acheive, f'(x) = -6x-5 Take the derivative to achieve, f'(x)=6x-5 Use the "a" value of f(x) as the slope, and state the slope is 3. Use the "b" value of f(x) and state that the...

Journalize the following transactions for the buyer, Bennett Company, using the gross method to account for purchase discounts. Assume a perpetual inventory system. July 7 July 13 July 17 Purchased...

EREGRINE - GLOBAL SERVICES Question 2 0 of 1 0 5 BA - Healthcare Management Exit Exam uman Resource Management - Accountability The attitude of an organization's \ ( \ qquad \ ) toward human capital...

The Skyline Motel opened for business on May 1, 2017. Its trial balance before adjustment on May 31 is as follows. SKYLINE MOTEL Trial Balance May 31, 2017 Account Number Debit Credit 101 Cash $...

1.What did you learned about precision and accuracy? 2. What did you enjoyed most in the topic precision and accuracy? 3. What do you want to learn more about precision and accuracy?

Suppose that a Markov chain has transition probability matrix 1 1(1/2 1/2 2 1/4 3/4 P (a) What is the long-run proportion of time that the chain is in state i, i = 1, 2 ? 5. What should r2 be if it...

On November 1, 2017, US Frigatebird Company sold an airplane worth S1 million Australian dollars to Australian company Heron Inc., to be paid on February 1, 2018 in Sydney. In order to hedge foreign...

Deduce the probability that a prospective homebuyer in Example 5.8 expresses no preference using the simple probabilities of the other outcomes. P (Prospective homebuyer makes no choice) =...

What proportion of 1- to 14-year-olds are hypertensive? Hypertension People are classified as hypertensive if their systolic blood pressure (SBP) is higher than a specified level for their age group,...

A survey of taxpayers who complete their own tax returns were asked the following questions. Determine the type of data each question produces. a. Did you use software? b. How long did it take you to...

A random sample of car owners was asked these questions. Identify the type of data. a. Make of car b. Age of your car in months c. Amount of annual insurance d. Number of miles on odometer

A company has bid on two large construction projects. The company president believes that the probability of winning the first contract is 0.70, the probability of winning the second contract is 0.4...

Corporate decision makers and analysts often use a particular technique, called a DuPont analysis , to better understand the factors that drive a companys financial performance, as reflected by its...

Assignment 1 Summary: Cash Flow Statement Analysis Download the annual report of a listed company from its corporate website. The annual report is a pdf document and may be found under the link...