A rectangular storage container without a lid is to have a volume of 10 m3. The length of its base is twice the width. Material for the base costs $15 per square meter. Material for the sides costs $9 per square meter. Find the cost (in dollars) of materials for the least expensive such container. (Round your answer to the nearest cent.)
A rectangular storage container without a lid is to have a volume of 10 m3. The length of its base is twice the width. Material for the base costs $15 per square meter. Material for the sides costs $9 per square meter. Find the cost (in dollars) of materials for the least expensive such container. (Round your answer to the nearest cent.)
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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![A rectangular storage container without a lid is to have a volume of 10 m3. The length of its base is twice the width. Material for the base costs $15 per square meter. Material for the sides costs $9 per square meter. Find the cost (in
dollars) of materials for the least expensive such container. (Round your answer to the nearest cent.)
$
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Please try again, keeping in mind that the volume of an open box with height h and a rectangular base whose length is twice its width w is V = 2w-h, and the cost function of its surface is C = c,(2w2) + c,[2(wh) + 2(2wh)], where c, is
the cost for the base and c, is the cost for the sides. Find a relationship between w and h, using the fact that the volume is a constant. Rewrite the cost function as a function of one variable. Use calculus to find the minimum possible
cost.
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Transcribed Image Text:A rectangular storage container without a lid is to have a volume of 10 m3. The length of its base is twice the width. Material for the base costs $15 per square meter. Material for the sides costs $9 per square meter. Find the cost (in
dollars) of materials for the least expensive such container. (Round your answer to the nearest cent.)
$
Enhanced Feedback
Please try again, keeping in mind that the volume of an open box with height h and a rectangular base whose length is twice its width w is V = 2w-h, and the cost function of its surface is C = c,(2w2) + c,[2(wh) + 2(2wh)], where c, is
the cost for the base and c, is the cost for the sides. Find a relationship between w and h, using the fact that the volume is a constant. Rewrite the cost function as a function of one variable. Use calculus to find the minimum possible
cost.
Need Help?
Read It
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