Log in
Mathematics
2
answers
0
watching
222
views

A farmer wants to fence in an area of 1.5 million square feet in a rectangular field and then divide it in half with a fence parallel to one of the sides of the rectangle. How can he do this so as to minimize the cost of the fence?

Watch
2
answers
0
watching
222
views

For unlimited access to Homework Help, a Homework+ subscription is required.

Unlock all answers

Get 1 free homework help answer.
Already have an account? Log in
Share
Reid Wolff
Reid WolffLv2
23 May 2020
Already have an account? Log in
Share

Related questions

A farmer w/ 750ft of fencing wants to enclose a rectangular area then divide it into four pens with fencing parallel to one side of the rectangle. What is the largest possible total area of the four pens?

Consider the following problem: 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. What is the largest possible total area of the four pens?

  1. Draw several diagrams illustrating the situation, some with shallow, wide pens and some with deep, narrow pens. Find the total areas of these configurations. Does it appear that there is a maximum area? If so, estimate it.

  2. Draw a diagram illustrating the general situation. Introduce notation and label the diagram with your symbols.

  3. Write an expression for the total area.

  4. Use the given information to write an equation that relates the variables.

  5. Use part (d) to write the total area as a function of one variable.

  6. Finish solving the problem and compare the answer with your estimate in part (a).

4. You are constructing a rectangular storage shed with a square base. You need space to accomodate 75 m of stuff. The floor is made of concrete which costs 2$/mĀ². The four walls are made of wood, which costs 5 $/mĀ². The roof tiles cost 4 $/m2 (a) Write a formula for the total cost of the shed in terms of a single variable. Indicate what this variable represents, and state its domain. (3 marks) (b) What should be the dimensions of the shed to minimize the cost? State the length, width and height, and also the minimum value of the cost. (5 marks) (c) Suppose you only have enough concrete to cover an area of 16 mĀ². How does this change the domain of the variable you chose in part (a)? (1 mark) (d) With the restriction from part (c), can you achieve the minimum cost you

Weekly leaderboard

Home
Homework Help 3,900,000
Mathematics 240,000
Start filling in the gaps now
Log in