1. Engineers are designing a box-shaped aquarium with a square bottom and an open top.The aquarium must hold 500 ft3 of water. What dimensions should they use to create anacceptable aquarium with the least amount of glass?a) Diagram (include variables)W Xb) Objective function (state equation):e4=500c) Constraints (state equation):_objecbived) Steps to the solution of the optimization problem using derivatives4 sides beye) Dimensions of the aquarium:f) Glass needed (ft2):

Answered: Image /qna-images/answer/5675c15b-251c-4ec0-9a71-6fd657836962.jpg

Engineers are designing a box-shaped aquarium with a square bottom and an open top. The aquarium must hold 500 ft3 of water. What dimensions should they use to create an acceptable aquarium with the least amount of glass?

Engineers are designing a box-shaped aquarium with a square bottom and an open top. The aquarium must hold 500 ft3 of water. What dimensions should they use to create an acceptable aquarium with the least amount of glass?

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter2: Systems Of Linear Equations

Section2.4: Applications

Problem 23EQ: 23. Consider a simple economy with just two industries: farming and manufacturing. Farming consumes...

See similar textbooks

Related questions

Q: A gutter with trapezoidal cross section is to be made from a long sheet of tin that is 18 inches…

A: Given that , Total length of the sheet = 18 inches find width across the top will give the greatest…

Q: A rectangular piece of cardboard, whose area is 198 square centimeters, is made into an open box by…

A: Let the length of the box is = x cm width= y cm. Given height= 2 cm So the volume=2xy

Q: Find the dimensions of a rectangle with area 343 m2 whose perimeter is as small as possible.

Q: One cake is rectangular with a length of 14 inches, a width of 10 inches, and a height of 2…

Q: A snack food company has decided to package its new brand of crackers in a box shaped like a…

A: Given data is : Volume=10834 cubic inches=108.75 inch3 Widthw=714inch=7.25inch Depth d=114 inch=1.25…

Q: Among all rectangles whose area is 400 m^2, which one has the smallest perimeter?

A: The objective of the question is determine the sides of the rectangle for which the perimeter is…

Q: A rectangular solar shipping container has a volume of 84 cubic meters. The client tells…

A: Let the width of the solar shipping container be x meter. Since length is one meter longer than the…

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

Q: Two equal rectangular lots are enclosed by fencing the perimeter of a rectangular lot and then…

A: Given problem is : Two equal rectangular lots are enclosed by fencing the perimeter of a rectangular…

Q: A training field is formed by joining a rectangle and two semicircles, as shown below. The rectangle…

Q: Engineers are designing a box-shaped aquarium with a square bottom and an open top. The aquarium…

Q: If a rectangular pool is 15 feet long and 8 feet wide and there are 20 people in the pool; what is…

A: Given, Length of pool l= 15 feet Width of pool w= 8 feet Number of people in the pool = 20

Q: 2. Find the dimensions of a rectangle with an area of 225 square cm, whose perimeter is as small as…

Q: A silo consists of a cylinder surmounted by a hemisphere. If the floor is three times as expensive…

A: Let r be the radius of the hemisphere. This is also the radius of the base of the cylinder. Let h be…

Q: What is the maximum capacity of a dumpster that is 8 meters long, 5 meters wide, and 4 meters high?

A: In the given question the maximum capacity is asked of a dumpster of which dimensions are as follows…

Q: Engineers are designing a box-shaped aquarium with a square bottom and an open top. The aquarium…

A: Given query is to find the dimensions of the aquarium for least amount of surface area.

Q: There are 170 boxes with equal sides and sizes. What would be the size of each box in order to fit…

Q: b. Engineers are designing a box-shaped aquarium with a square bottom and an open top. The aquarium…

Q: The cabinet that will enclose the Acrosonic model D loudspeaker system will be rectangular and will…

Q: a rectange is 4 inches longer than it is wide. numerically its area exceeds its perimeter by 17.…

Q: What are the dimensions for the cheapest possible rectangular box with a volume of 56 cm if the…

A: Consider the provided question, Let length of the box = l cm Width of the box = w cm And, height of…

Q: A cube shaped box has a volume of 125 inches. If the box is packed full of cubes with edge lengths…

A: Vbigger box = 125 cubic inchEdge length of small cube = 1 inchVolume of one small cube, Vsmall cube…

Q: The diameter of a standard basketball is 9.5 inches. If the basketballs are covered in rubber, what…

A: *As per the guidelines, only the first question answered. Please repost the remaining questions…

Q: A rectangular piece of cardboard, whose area is 143 square centimeters, is made into an open box by…

Q: The factory director wants to increase the volume of coconut water sold per container. State whether…

Q: The Central Park Zoo needs to build a rectangular area of 225 sq. feet to holda zebra, a lion, a…

Q: A small heater has a rectangular filter that has a width of 24.0 in. and a length of 30.0 in.…

Q: Find the dimensions of a rectangle with area 1,728 m² whose perimeter is as small as possib m…

Q: A rectangular display in a furniture store needs walls on three sides only, with 6-foot openings on…

A: Given, The display needs to have floor space of 450 ft2. Used formula - Area of rectangle = Length…

Q: If a rectangular garden is 6 feet long and 4 feet wide and there are 10 vegetables planted; what is…

Q: A snack food company has decided to package its new brand of crackers in a box shaped like a…

A: The volume of the box is 108 3/4 cubic inches. Volume=108 34 in3=108.75 in3Width=714 in=7.25…

Q: if the mass of a cube were 48G and it’s volume 24CM3 what would be its density

A: Given, mass=48g Volume=24cm3

Q: The U.S Post Office will accept a box for shipping only if the sum of the length and girth (distance…

Q: A country with one of the highest population densities is San Wan, where approximately 34,000…

A: Population density is the number of people divided by the size of the area. Here, number of…

Q: Building Play Area

Q: A rectangular price tag has a perimeter of 20 centimeters and an area of 21 centimeters. What are…

A: Given: A rectangular price tag has a perimeter of 20 centimeters and an area of 21 centimeters.

Q: In order to properly feed her animals, a rancher needs to enclose a total area of 4704 square feet…

Q: An aquarium with rectangular sides and bottom (and no top) is to hold 5 gal. Find its proportions so…

A: Let the dimensions of a rectangular aquarium is Length =l Width=w Height=h Now, The volume is,…

Q: Three of the sides will require fencing and the fourth wall already exists.If the farmer has 164…

Q: An office, 5 m long, 4 m wide and 2.5 m high, is to have its walls covered with plywood panels. The…

Q: Engineers are designing a box-shaped aquarium with a square bottom and an open top. The aquarium…

Q: A rectangular field is fenced off, an existing wall being used as one side. If the area of the field…

A: Suppose, L is the length and W is the width of the rectangular field. Then Area A=L×W But, area is…

Q: An architect needs to design a rectangular room with an area of 89ft2 . What dimension should be use…

Q: The owner of a cattle ranch would like to fence in a rectangular area of 3000000 m² and then divide…

A: It is given that a rectangular area is 3000000 m2 The area of rectangle is A=l⋅b, where l and b are…

Q: A gutter with trapezoidal cross section is to be made from a long sheet of tin that is 15 inches…

A: Trapezoidal and geometrical area

Q: Golf balls are usually dimpled. Does a dimpled golf ball have more surface area than a smooth golf…

A: Dimples reduce the drag exerted on the ball. A dimpled ball experiences about half of drag…

Q: Suppose you ask a jeweller to form a gold in the shape of a sphere whose volume is * cm³. But you…

A: Intial volume of gold = 4π/3.

Q: Three of the sides will require fencing and the fourth wall already exists.If the farmer has 132…

Q: What is the length and width of a rectangle that has an area of 64 square ft and a minimum…

A: let length = x width = y Area = 64 square ftxy=64y=64x

Q: Find the dimensions of a rectangle with area 1,000 m² whose perimeter is as small as possible. (If…

A: According to question,

Question

1. Engineers are designing a box-shaped aquarium with a square bottom and an open top.
The aquarium must hold 500 ft3 of water. What dimensions should they use to create an
acceptable aquarium with the least amount of glass?
a) Diagram (include variables)
W X
b) Objective function (state equation):
e4=500
c) Constraints (state equation):_
objecbive
d) Steps to the solution of the optimization problem using derivatives
4 sides bey
e) Dimensions of the aquarium:
f) Glass needed (ft2):

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Step 3

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 3 steps with 3 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Inequality$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.