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Outcome: Find the absolute maximum or minimum value of a quantity subject to given constraints. MATH 2413: Calculus I - Activity 10 1. Postal regulations limit the girth plus length of a box to 108 inches ("girth" is the perimeter of the smallest end). What are the dimensions of the largest box with a square end that can be mailed? (a) Let z be the length of one side of the square end and y the length of the longer side. Label these below. (b) What quantity does this problem ask to maximize? Find a formula for this quantity in terms of and y (c) The largest such box's girth plus length equals 108 inches. Write this as an equation involving z and y (d) Use your equation from (e) to rewrite your formula from (b) as a function of I only

Outcome: Find the absolute maximum or minimum value of a quantity subject to given constraints. MATH 2413: Calculus I - Activity 10 1. Postal regulations limit the girth plus length of a box to 108 inches ("girth" is the perimeter of the smallest end). What are the dimensions of the largest box with a square end that can be mailed? (a) Let z be the length of one side of the square end and y the length of the longer side. Label these below. (b) What quantity does this problem ask to maximize? Find a formula for this quantity in terms of and y (c) The largest such box's girth plus length equals 108 inches. Write this as an equation involving z and y (d) Use your equation from (e) to rewrite your formula from (b) as a function of I only

Calculus: Early Transcendentals
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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could you do c please

**Outcome:** Find the absolute maximum or minimum value of a quantity subject to given constraints. **MATH 2413: Calculus I – Activity 10** 1. Postal regulations limit the girth plus length of a box to 108 inches (“girth” is the perimeter of the smallest end). What are the dimensions of the largest box with a square end that can be mailed? (a) Let \( x \) be the length of one side of the square end and \( y \) the length of the longer side. Label these below. - *Diagram Description:* The image shows a three-dimensional box with a square end. The sides of the square are labeled as \( x \), and the longer side of the box is labeled as \( y \). (b) What quantity does this problem ask to maximize? Find a formula for this quantity in terms of \( x \) and \( y \). (c) The largest such box’s girth plus length equals 108 inches. Write this as an equation involving \( x \) and \( y \). (d) Use your equation from (c) to rewrite your formula from (b) as a function of \( x \) only. (e) Based on what \( x \) represents in this problem, what is the domain of this function? (f) Use Calculus to find the dimensions of the largest such box that can be mailed. Include units.
Transcribed Image Text:**Outcome:** Find the absolute maximum or minimum value of a quantity subject to given constraints. **MATH 2413: Calculus I – Activity 10** 1. Postal regulations limit the girth plus length of a box to 108 inches (“girth” is the perimeter of the smallest end). What are the dimensions of the largest box with a square end that can be mailed? (a) Let \( x \) be the length of one side of the square end and \( y \) the length of the longer side. Label these below. - *Diagram Description:* The image shows a three-dimensional box with a square end. The sides of the square are labeled as \( x \), and the longer side of the box is labeled as \( y \). (b) What quantity does this problem ask to maximize? Find a formula for this quantity in terms of \( x \) and \( y \). (c) The largest such box’s girth plus length equals 108 inches. Write this as an equation involving \( x \) and \( y \). (d) Use your equation from (c) to rewrite your formula from (b) as a function of \( x \) only. (e) Based on what \( x \) represents in this problem, what is the domain of this function? (f) Use Calculus to find the dimensions of the largest such box that can be mailed. Include units.
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