Lone Depot and Homes are two competing home improvement stores. Each claims to provide customers with a cost effective, versatile rectangular storage container with a square base and a volume of 36 ft³ (see the diagram below). Each company has determined they want to use the same type of materials to construct the containers. The material for the sides and top of each container costs $2/ft2, and the material for the bottom costs $4/ft². Lone Depot claims that the minimum cost of producing such a container with the desired volume of 36 ft3 can be obtained if the dimensions of the container are 2.5 ft by 2.5 ft by 5.76 ft. However, Homes claims that the minimum cost of producing such a container can be obtained if the dimensions of the container are 4 ft by 4 ft by 2.25 ft. x 1. Which company's proposed dimensions are better? In other words, which will result in a lower cost of constructing each container? a) Mathematically justify your answer. For each store, you must draw at least two rectangles with labeled dimensions to represent the surfaces that you are finding the area of. b) Write a paragraph explaining your work and answer.
Lone Depot and Homes are two competing home improvement stores. Each claims to provide customers with a cost effective, versatile rectangular storage container with a square base and a volume of 36 ft³ (see the diagram below). Each company has determined they want to use the same type of materials to construct the containers. The material for the sides and top of each container costs $2/ft2, and the material for the bottom costs $4/ft². Lone Depot claims that the minimum cost of producing such a container with the desired volume of 36 ft3 can be obtained if the dimensions of the container are 2.5 ft by 2.5 ft by 5.76 ft. However, Homes claims that the minimum cost of producing such a container can be obtained if the dimensions of the container are 4 ft by 4 ft by 2.25 ft. x 1. Which company's proposed dimensions are better? In other words, which will result in a lower cost of constructing each container? a) Mathematically justify your answer. For each store, you must draw at least two rectangles with labeled dimensions to represent the surfaces that you are finding the area of. b) Write a paragraph explaining your work and answer.
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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![Lone Depot and Homes are two competing home improvement stores. Each claims to provide customers
with a cost effective, versatile rectangular storage container with a square base and a volume of 36 ft³ (see
the diagram below).
Each company has determined they want to use the same type of materials to
construct the containers. The material for the sides and top of each container
costs $2/ft², and the material for the bottom costs $4/ft².
Lone Depot claims that the minimum cost of producing such a container with
the desired volume of 36 ft³ can be obtained if the dimensions of the container
are 2.5 ft by 2.5 ft by 5.76 ft. However, Homes claims that the minimum cost of
producing such a container can be obtained if the dimensions of the container
are 4 ft by 4 ft by 2.25 ft.
x
x
1. Which company's proposed dimensions are better? In other words, which will result in a lower cost of
constructing each container?
a) Mathematically justify your answer. For each store, you must draw at least two rectangles with
labeled dimensions to represent the surfaces that you are finding the area of.
b) Write a paragraph explaining your work and answer.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2a2a452a-da4a-454c-9576-b485e15495e5%2F3e506064-8e10-475b-ab65-b999716b6d84%2Fw42oux6_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Lone Depot and Homes are two competing home improvement stores. Each claims to provide customers
with a cost effective, versatile rectangular storage container with a square base and a volume of 36 ft³ (see
the diagram below).
Each company has determined they want to use the same type of materials to
construct the containers. The material for the sides and top of each container
costs $2/ft², and the material for the bottom costs $4/ft².
Lone Depot claims that the minimum cost of producing such a container with
the desired volume of 36 ft³ can be obtained if the dimensions of the container
are 2.5 ft by 2.5 ft by 5.76 ft. However, Homes claims that the minimum cost of
producing such a container can be obtained if the dimensions of the container
are 4 ft by 4 ft by 2.25 ft.
x
x
1. Which company's proposed dimensions are better? In other words, which will result in a lower cost of
constructing each container?
a) Mathematically justify your answer. For each store, you must draw at least two rectangles with
labeled dimensions to represent the surfaces that you are finding the area of.
b) Write a paragraph explaining your work and answer.
![Determine whether either of these company's dimensions are the best. In other words, determine the
dimensions that would minimize the cost of producing each storage container, as well as the minimum
cost.
C. Show all of your work as we did in-class.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2a2a452a-da4a-454c-9576-b485e15495e5%2F3e506064-8e10-475b-ab65-b999716b6d84%2Fdy67nfs_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Determine whether either of these company's dimensions are the best. In other words, determine the
dimensions that would minimize the cost of producing each storage container, as well as the minimum
cost.
C. Show all of your work as we did in-class.
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Step 1: Define the problem
VIEWStep 2: Draw the figure for each stores
VIEWStep 3: Describe the work
VIEWStep 4: Determine the cost function in terms of x
VIEWStep 5: Determine the derivative of C(x)
VIEWStep 6: Determine the critical values
VIEWStep 7: Determine the second derivative test
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