2. In order to package one of their products, Acme Box Co. needs to construct a box whose bottom side has length 3 times its width. The material used to build the top and bottom of the box cost $10 per square foot, while the material used to build the four sides of the box cost $6 per square foot. The box must have a volume of 50 cubic feet. (a) In terms of the length l of the bottom, the width w of the bottom and the height h of the box (all measured in feet), write a formula for the cost C (in dollars) to construct a box of length l, width w and height h. (b) Given the other conditions specified in the problem, express C as a function of a single variable. (c) Determine the dimensions of the box that minimize the cost. Be sure to justify that you have found dimensions that produce the minimum cost. (You'll be fired if you submit the maximum cost to your boss!!) To the nearest dollar, how much will it cost to build the box at these dimensions?

2. In order to package one of their products, Acme Box Co. needs to construct a box whose bottom side has length 3 times its width. The material used to build the top and bottom of the box cost $10 per square foot, while the material used to build the four sides of the box cost $6 per square foot. The box must have a volume of 50 cubic feet. (a) In terms of the length l of the bottom, the width w of the bottom and the height h of the box (all measured in feet), write a formula for the cost C (in dollars) to construct a box of length l, width w and height h. (b) Given the other conditions specified in the problem, express C as a function of a single variable. (c) Determine the dimensions of the box that minimize the cost. Be sure to justify that you have found dimensions that produce the minimum cost. (You'll be fired if you submit the maximum cost to your boss!!) To the nearest dollar, how much will it cost to build the box at these dimensions?

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 40E: As in Exercise 39, find the volume of the box if four congruent squares with sides of length 6 in....

See similar textbooks

Similar questions

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?
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.
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?
Zaidah plans a raised flower bed 2 ft high by 12 ft wide by 15 ft long. The mulch, soil, and peat mixture used to fill the raised bed costs 15.75 per cubic yard. What is the total cost of the ingredients used to fill the raised garden?
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?