Alina wants to make keepsake boxes for her two best friends. She doesn't have a lot of money, so she wants to make each box described so that it holds as much as possible with alimited amount of material.For Eliza, Alina wants to make a rectangular box whose base is twice as long as it is wide. This box will be lined on the entire inside with velvet and in addition the outside of the top ofthe box is to be lined in velvet. If Alina has 300 square inches of velvet, how can she make Eliza's box so that it holds as many keepsakes as possible? Find the width (w), length (/), andheight of the box in inches. (Round your answers to three decimal places.)Velvet-lined boxwidthlengthheighteBook1=2winininW

Answered: Alina wants to make keepsake boxes for…

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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Similar questions

The Greenville Public Library just received a grant to renovate their children's reading room. Before any work begins, the librarians need to pack all of their picture books into cardboard boxes to keep them safe. They estimate that each book weighs an average of 12 ounces. To make sure the boxes are not too heavy, they only plan to put 15 pounds of books in each box. If the library has 1,200 picture books, how many boxes do the librarians expect to need? Hint: There are 16 ounces in 1 pound.
The cost of the material for the top and bottom of a cylindrical can is 10 cents per square inch. The material for the rest of the can costs 5 cents per square inch. If the can must hold 500 cubic inches of liquid, what dimensions should be chosen to make the cheapest can?
A group of friends is roping off a soccer field in a back yard. A particular full-size soccer field is a rectangle with a length of 130 yards and a width of 70 yards. To fit the field in the back yard, the group needs to reduce the size of the field so its perimeter is 160 yards. What is the area of the soccer field in the back yard? The area of the field in the back yard is square yards.
Hugo and Boss are upgrading the storage in their backyard. The existing storage has the shape of a rectangular prism with the dimensions 1m by 2m by 4m. By what amount, x, should they increase each dimension so that the new storage is 9 times the volume of the original storage?
A gallon of latex paint can cover 250 square feet. Maria has a rectangular room whose dimensions are 20 feet by 22 feet, with 9-foot ceilings. How many gallon containers of paint does she need to buy to paint two coats on each wall?
Box A and box B, each contain type C connectors. Box A contains 200 connectors and costs $30. Find the cost of box B, which contains 260 connectors. The unit price is the same for both boxes.
A rectangular storage container has a lid that is made from the same material as thesides, and is to have a volume of 10 m3. The length of its base is twice the width.Material for the base costs $10 per square meter. Material for the sides costs $6 persquare meter. Find the cost of materials for the cheapest such container.
A fence is to be built to enclose a rectangular area of 300 square feet. The fence along three sides is to be made of material that costs 6 dollars per foot, and the material along the fourth side costs 12 dollars per foot. Find the length and width of the enclosure that is most economical to construct.
Two collaborators, Nicolas and Felipe, are talking about the order they received with the size of four new pieces that will be produced. Each of the collaborators received the request on a piece of paper, but both were careless and ended up missing some information. Before asking for information about the order, they decided to talk and try to find out which measures were missing. Nicolas' paper only has the average length, which is 17.2 meters. The paper with the order that Felipe has, about the same pieces, contains the information that the median length is 17.0 meters. From the data they have, they were able to correctly conclude that the average between the lengths of the largest and smallest piece is:
A rectangular lidless bin must hold 10 m3 of garbage. Its base is twice as long as it is wide. The metal used for the base costs $5 per square meter, whereas metal for the sides costs $3 per square meter. Find the lowest cost for a bin which meets these specifications. (Round your answer to the nearest cent.)

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