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 y 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. 2. 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. a) Show all of your work as we did in-class. b) Once you have completed part a), record yourself explaining your work and answer to #2a. Assume that you are talking to another college student who has not taken calculus yet. Record yourself explaining why you chose to do the calculations that you did for #2a and thoroughly explain each step of your work as if you were teaching this concept to them. When creating your recording, you are asked to show your solution to #2a so that you can point to your work as you explain it. This is anticipated to be a short video (approximately 2-4 minutes).
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 y 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. 2. 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. a) Show all of your work as we did in-class. b) Once you have completed part a), record yourself explaining your work and answer to #2a. Assume that you are talking to another college student who has not taken calculus yet. Record yourself explaining why you chose to do the calculations that you did for #2a and thoroughly explain each step of your work as if you were teaching this concept to them. When creating your recording, you are asked to show your solution to #2a so that you can point to your work as you explain it. This is anticipated to be a short video (approximately 2-4 minutes).
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 37E: Zaidah plans a raised flower bed 2 ft high by 12 ft wide by 15 ft long. The mulch, soil, and peat...
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Please do question 2b in written format instead of video. Thanks.
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
y
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.
Transcribed Image Text:2. 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.
a) Show all of your work as we did in-class.
b) Once you have completed part a), record yourself explaining your work and answer to #2a.
Assume that you are talking to another college student who has not taken calculus yet. Record
yourself explaining why you chose to do the calculations that you did for #2a and thoroughly
explain each step of your work as if you were teaching this concept to them. When creating
your recording, you are asked to show your solution to #2a so that you can point to your work
as you explain it. This is anticipated to be a short video (approximately 2-4 minutes).
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