A covered box is to be made from a ectangular sheet of cardboard measuring 25 inches by 40 inches. This is done by cutting out the shaded regions of the figure and then folding on the dotted lines. What are the dimensions x, y, and z that maximize the volume? X= y = Z= inches inches inches ...
A covered box is to be made from a ectangular sheet of cardboard measuring 25 inches by 40 inches. This is done by cutting out the shaded regions of the figure and then folding on the dotted lines. What are the dimensions x, y, and z that maximize the volume? X= y = Z= inches inches inches ...
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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![### Creating a Covered Box from Cardboard
A covered box is to be made from a rectangular sheet of cardboard measuring 25 inches by 40 inches. This box is constructed by cutting out the shaded regions of the figure (shown in blue) and then folding along the dotted lines.
#### Objective:
Determine the dimensions \( x \), \( y \), and \( z \) that maximize the volume of the box.
##### Diagram Explanation:
- The rectangular sheet shows sections marked for cutting and folding.
- \( x \) represents the height of the side flaps which are to be folded up.
- \( y \) represents the length of the box after folding.
- \( z \) represents the width of the box after folding.
- Two shaded sections on each end of the rectangle (of width \( x \)) are cut out.
- Two shaded sections along the sides (of width \( z \)) are cut out.
##### User Input:
In order to solve for the dimensions that maximize the volume, input the values of x, y, and z.
```
x = [ ] inches
y = [ ] inches
z = [ ] inches
```
Complete the input fields to calculate the dimensions that would provide the maximum volume for the box from the given cardboard sheet.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F22969543-4b1b-47a8-98d2-f1e5e1e74392%2F727347ae-e03e-49d5-ba3b-f0198407846e%2Fjpdy2m5_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Creating a Covered Box from Cardboard
A covered box is to be made from a rectangular sheet of cardboard measuring 25 inches by 40 inches. This box is constructed by cutting out the shaded regions of the figure (shown in blue) and then folding along the dotted lines.
#### Objective:
Determine the dimensions \( x \), \( y \), and \( z \) that maximize the volume of the box.
##### Diagram Explanation:
- The rectangular sheet shows sections marked for cutting and folding.
- \( x \) represents the height of the side flaps which are to be folded up.
- \( y \) represents the length of the box after folding.
- \( z \) represents the width of the box after folding.
- Two shaded sections on each end of the rectangle (of width \( x \)) are cut out.
- Two shaded sections along the sides (of width \( z \)) are cut out.
##### User Input:
In order to solve for the dimensions that maximize the volume, input the values of x, y, and z.
```
x = [ ] inches
y = [ ] inches
z = [ ] inches
```
Complete the input fields to calculate the dimensions that would provide the maximum volume for the box from the given cardboard sheet.
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