A box with a square base and open top must have a volume of 100 cm3 . The material for the bottom costs 5 cents per cm2 and the material for the sides costs 3 cents per cm2 . Find the dimensions of the box that minimize the cost of material used.

A box with a square base and open top must have a volume of 100 cm3 . The material for the bottom costs 5 cents per cm2 and the material for the sides costs 3 cents per cm2 . Find the dimensions of the box that minimize the cost of material used.

Elementary Geometry For College Students, 7e

7th Edition

ISBN:9781337614085

Author:Alexander, Daniel C.; Koeberlein, Geralyn M.

Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.

Chapter9: Surfaces And Solids

Section9.1: Prisms, Area And Volume

Problem 27E: The box with dimensions indicated is to be constructed of materials that cost 1 cent per square inch...

See similar textbooks

Related questions

Q: A farmer wants to build a rectangular pen and then divide it with two interior fences. The total…

Q: A cylindrical container that is open at the top is to be made from two kinds of material. The…

Q: A box with a square base and an open top must have a volume of 96 cubic inches. If the bottom is…

A: Given that the box has a square base and is open at the top. Since the base of the box is a square,…

Q: A box with a square base and a top is to made to enclose 160 cubic inches. The cost of the material…

Q: A fence is to be built to enclose a rectangular area of 200 square feet. The fence along three sides…

A: For relative maximum or minimum To maximize or minimize a function f(x) 1st we need to find its…

Q: A fence is to be built to enclose a rectangular area of 220 square feet. The fence along three sides…

Q: A fence is to be built to enclose a rectangular area of 210 square feet. The fence along three sides…

A: Let us consider the fence of rectangular area of 210 square feet. Let us consider the length of…

Q: A closed rectangular box with a volume of 16 ft is made from two kinds of materials. The top and…

A: We will use Lagrange Multiplier method to maximize / minimize a function f(x,,y,z) subject to…

Q: A closed rectangular box is to have a volume of 250 cubic centimeters. If the material for the top…

A: Given: Volume=250 cm3

Q: A fence is to be built to enclose a rectangular area of 250 square feet. The fence along three sides…

A: let the lengh of a rectangle is l and width is bthen area of rectangle=lbaccording to…

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

A: I have solved with detail and find the dimensions.Given the final solution in boxes.

Q: A fence is to be built to enclose a rectangular area of 280 square feet. The fence along three sides…

A: step1 Given Rectangle of Area =280 sq feat.Let 'x' - Length , 'y' - Breadth

Q: A fence is to be built to enclose a rectangular area of 260 square feet. The fence along three sides…

A: Given that ractanguler area is 260 square feet.and the fence along three side is to be made of…

Q: A rectangular box has base with one side three times the length of the other side. If the top of the…

Q: An industrial tank is to be formed by adjoining two hemispheres to the ends of a right circular…

Q: If the garden is to be 1800 square feet, and the fence along the driveway costs $6 per foot while on…

A: Let x ( in feet) be the length of the garden along driveway and y (in feet) be the length…

Q: A cylinder shaped can needs to be constructed to hold 300 cubic centimeters of soup. The material…

Q: An open-topped storage box with a square base has a capacity of 5 m3. The material for the sides…

Q: A rectangular box without a lid must be made at a cost of $15 for stuff. If the material for the…

A: I am going to solve the given problem by using some simple algebra to get the required result.

Q: A trash company is designing an open-top, rectangular container that will have a volume of 625 ft.…

A: A trash company is designing on open top rectangular container having volume = 625 ft3 Let length…

Q: We want to construct a box whose base length is 3 times the base width. If the box must have a…

A: Minimization of surface area

Q: A cylinder shaped can needs to be constructed to hold 400 cubic centimeters of soup. The material…

A: We know that the total surface area of a cylinder with radius r and height h, is A=2πrh+r. Volume of…

Q: A fence is to be built to enclose a rectangular area of 320 square feet. The fence along three sides…

Q: A farmer wants to fence an area of 13.5 million square feet in a rectangular field and then divide…

Q: A box with a square base and a closed top has a volume of 20 cubic ft. the cost of material for the…

A: Given: Volume of square base = 20 cubic feet.…

Q: If the garden is to be 1800 square feet, and the fence along the driveway costs $6 per foot while on…

A: Given, Area of the garden = 1800 square feet

Q: A box with a volume of 530 cm3530 cm3 is to be constructed. The sides of the box cost 3 cents per…

A: Given, Volume of the box = 530 cm3 Sides of the box cost = 3 cents/cm2 Top and bottom cost = 6…

Q: A square-based, box-shaped shipping crate is designed to have a volume of 16ft. The material used to…

Q: You are to construct an open rectangular box with a square base and a volume of 48 ft3. If material…

A: The question contains two parts.First find the dimension of the least expensive box. In second part…

Q: Emily is making a closed rectangular box with a square base from two different woods. The wood for…

A: The solver program in the Excel can be used to optimize a function within specific constraints. The…

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

A: Given query is to find the dimensions of the gardern to minimize the cost.

Q: A fence is to be built to enclose a rectangular area of 250 square feet. The fence along three sides…

Q: The Engineer wanted to enclose a rectangular backyard on one side by a wooden fence costing…

Q: the base of an aquarium with given volume V is made of slate and the sides are made of glass. if the…

Q: A closed rectangular box is made with two kinds of materials. The top and bottom are made with…

Q: A box with a volume of 512cm3 is to be constructed. The sides of the box cost 2 cents per cm2, and…

A: Given the volume of the box is

Q: A rectangular field with one side along a river is to be fenced. Suppose that no fence is needed…

Q: A square-based, box-shaped shipping crate is designed to have a volume of 36 cubic feet. The…

A: Volume=x2y=36 ............equation(1) Cost=2x22k+4xyk Cost=4kx2+xy........equation(2) Form equation…

Q: Find the minimum cost of a rectangular box that is three times as long as it is wide and which holds…

A: Consider the dimension of rectangular box be x, 3x, and h. Then, volume is given by V=x×3x×h =3x2h…

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

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

Q: A rectangular box is to have a square base and a volume of 20 ft³. If the material for the base…

A: Given, Rectangular box is to have a square base and a volume of 20 ft3 The material for the base…

Q: The base of a rectangular prism shaped aquarium without a lid is made of slate and the sides are…

A: Given V=96 m3 Let the dimension is x, y and z Hence, Volume is given by V=xyz......1 The equation…

Q: the garden is to be 200 square feet, and the fence along the driveway costs $6 per foot while on the…

Q: A farmer wants to fence an area of 24 million square feet in a rectangular field and then divide it…

A: let the fencing done on a rectangular field with half of a fence done on a parallel side of a…

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

Q: An aquarium is to be constructed to hold 2160 in The base is to made of slate and the sides of…

Q: A farmer wants to fence an area of 37.5 million square feet in a rectangular field and then divide…

A: Consider the given information.

Question

A box with a square base and open top must have a volume of 100 cm3
. The
material for the bottom costs 5 cents per cm2
and the material for the sides costs 3 cents
per cm2
. Find the dimensions of the box that minimize the cost of material used.

Expert Solution

This question has been solved!

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

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Step by step

Solved in 2 steps with 2 images

SEE SOLUTION Check out a sample Q&A here

Similar questions

The box with dimensions indicated is to be constructed of materials that cost 1 cent per square inch for the lateral surface and 2 cents per square inch for the bases. What is the total cost of constructing the box?
For a right circular cone, the dimensions are r=6 cm and h=8 cm. If the length of the radius is doubled while the height is made half as large in forming a new cone, will the volumes of the two cones be equal?
Mary Frances has a rectangular garden plot that encloses an area of 48 yd2. If 28 yd of fencing are purchased to enclose the garden, what are the dimensions of the rectangular plot?
A cylindrical storage tank has a depth of 5 ft and a radius measuring 2 ft. If each cubic foot can hold 7.5 gallon of gasoline, what is the total storage capacity of the tank measured in gallons?