Thanks! O You're building a rectangular box. The material for the bottom costs $0.60 persquare foot, and the material for the sides and the top cost $0.20 per square foot.a) Find the dimensions to maximize the volume for such a box if the totalamount of money available for material is $12.b) Find the total volume of the box.Answer with a sentence and use appropriate units. Hint: This problem worksnicely using LaGrange Multipliers.

Name: Thanks! O You're building a rectangular box. The material for the bott
Uploaded: 2024-03-20T07:07:37.000Z
Channel: Bartleby
Description: Thanks! O You're building a rectangular box. The material for the bottom costs $0.60 persquare foot, and the material for the sides and the top cost $0.20 per square foot.a) Find the dimensions to maximize the volume for such a box if the totalamount

Answered: Image /qna-images/answer/2b87021a-ae2f-41ae-b670-980bb5af3d98.jpg

Answered: Thanks!

Math

Calculus

Thanks!

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 39E: Kristine creates an open box by cutting congruent squares from the four corners of a square piece of...

See similar textbooks

Similar questions

A storage shed is in the shape of a trapezoidal prism. Each trapezoid represents one of its bases. With dimensions as shown, what is the storage capacity volume of its interior?
The tin can shown at the right has the indicated dimensions. Estimate the number of square inches of tin required for its construction. HINT: Include the lid and the base in the result.
As in Exercise 39, find the volume of the box if four congruent squares with sides of length 6 in. are cut from the corners of a rectangular piece of poster board that is 20 in. wide by 30 in. long. Kristine creates an open box by cutting congruent squares from the four corners of a square piece of cardboard that has a length of 24 in. per side. If the congruent squares that are removed have sides that measure 6 in. each, what is the volume of the box formed by folding and sealing the flaps?
The farmer in Exercise 33 has decided to take the fencing purchased and use it to enclose the subdivided plots shown. aWhat are the overall dimensions of the rectangular enclosure shown? bWhat is the total area of the enclosure shown?
Kristine creates an open box by cutting congruent squares from the four corners of a square piece of cardboard that has a length of 24 in. per side. If the congruent squares that are removed have sides that measure 6 in. each, what is the volume of the box formed by folding and sealing the flaps?
The surface of a soccer ball is composed of 12 regular pentagons and 20 regular hexagons. With each side of each regular polygon measuring 4.5 cm, the area of each regular pentagon is 34.9 cm2 and area of each regular hexagon is 52.5 cm2. a What is the surface area of the soccer ball? b If the material used to construct the ball costs 0.8 of a cent per square centimeter, what is the cost of the materials used in construction?
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?
When the length of each edge of a cube is increased by 1 cm, the volume is increase by 61 cm3. What is the length of each edge of the original cube?
A pencil cup with a capacity of 80 in^3 is to be constructed in the shape of a rectangular Box with a square base and in open top. If the material for the sides costs 20 cents/in^2 in the material for the base costs 50 cents/in^2 , what should the dimensions of the cup be to minimize the construction cost? height= length= width=
Two containers designed to hold water are side by side, both in the shape of a cylinder. Container A has a diameter of 4 feet and a height of 13 feet. Container B has a diameter of 6 feet and a height of 8 feet. Container A is full of water and the water is pumped into Container B until Container A is empty.After the pumping is complete, what is the volume of the empty portion of Container B, to the nearest tenth of a cubic foot? play