# Calculus 1

a rectangular storage area is to be constructed along the sides of a tall building. A security fence is required along the three remaining sides of the area. What is the maximum area that can be enclosed with 1000m fencing?

1. 👍 0
2. 👎 0
3. 👁 107
1. 500x250

1. 👍 0
2. 👎 0
posted by Steve
2. @ Steve I don't completely understand I want to knowhow we got to that answer/

1. 👍 0
2. 👎 0
posted by Ally
3. well, draw a diagram. If the width is x, then the length is 1000-2x. So, the area is

a = x(1000-2x) = 1000x-2x^2
da/dx = 1000-4x
da/dx=0 when x=250

As is usual, you will find that for maximum area, the fencing is divided equally among the widths and lengths. In this case, that means 500 ft each.
2 widths of 250' each, and 1 length of 500.

Naturally, for a 4-sided enclosure, that just means a square.

1. 👍 0
2. 👎 0
posted by Steve
4. Ok thanks I don't quite get it but I will follow your steps and Draw the diagram :)

1. 👍 0
2. 👎 0
posted by Ally

## Similar Questions

1. ### Calculus

a rectangular storage area is to be constructed along the sides of a tall building. A security fence is required along the three remaining sides of the area. What is the maximum area that can be enclosed with 1000m fencing?

asked by Kenny on May 21, 2014
2. ### Calculus

a rectangular storage area is to be constructed along the sides of a tall building. A security fence is required along the three remaining sides of the area. What is the maximum area that can be enclosed with 1000m fencing?

asked by Ally on May 20, 2014
3. ### AP Calculus

The management of a large store has 1600 feet of fencing to fence in a rectangular storage yard using the building as one side of the yard. If the fencing is used for the remaining 3 sides, find the area of the largest yard

asked by Sarah on December 14, 2014
4. ### diff calculus

1.) triangular corner lot has perpendicular sides of lengths 120 feet and 160 feet. Find the dimensions of the largest rectangular building that can be constructed on the lot with sides parallel to the streets.

asked by west on October 17, 2014
5. ### Calculus AB/AP

A tank with a rectangular base and rectangular sides is to be open at the top. It is to be constructed so that its width is 4 meters and its volume is 36 cubic meters. If building the tank costs \$8 per square meter for the base

asked by Julie on November 28, 2011
6. ### AP CaLC. AB

1. A fence 8 ft tall runs parallel to a tall building at a distance of 7 ft from the building. What is the length of the shortest ladder that will reach from the ground over the fence to the wall of the building? Round the result

asked by Rachel on January 2, 2015
7. ### Algebra 1

First of all, we're learning how to solve equations with variables on both sides. Write and solve an equation for the situation. An architect is designing a rectangular greenhouse. Along one wall is a 7-ft storage area and 5

asked by Mercedez on November 3, 2011

Construction of a new plant: Architect's fees \$ 4,000 Cash paid for land and run-down building thereon 120,000 Removal of old building 18,000 Salvage from sale of old building parts (4,000) Survey to site the new building 800

asked by aa on June 30, 2010
9. ### Math

company will enclose a rectangular area of 12 comma 600 ft squared12,600 ft2 in the rear of its plant. One side will be bounded by the building and the other three sides by​ fencing, as shown to the right. If 320 ft320 ft of

asked by Wael on March 11, 2016
10. ### math

A box with a rectangular base and rectangular sides is to be open at the top. It is to be constructed so that its width is 8 meters and its volume is 72 cubic meters. If building this box costs \$20 per square meter for the base

asked by maricela on May 9, 2007

More Similar Questions