A closed box with a square base is to have a volume of 16, 000 cm?. The material for the top and bottom of the box cost $3 per square centimeter, while the material for the sides costs $1.50 per square centimeter. Let x be the length of the side of the square base. a). Write an expression for the height of the box in terms of x, b). Set up the cost C(x) as a function of x, find the domain. c). Find C'(x), and find the critical number(s). d). Find the a value and the dimension of the box that will lead to the minimum total cost. e). What is the minimum cost?
A closed box with a square base is to have a volume of 16, 000 cm?. The material for the top and bottom of the box cost $3 per square centimeter, while the material for the sides costs $1.50 per square centimeter. Let x be the length of the side of the square base. a). Write an expression for the height of the box in terms of x, b). Set up the cost C(x) as a function of x, find the domain. c). Find C'(x), and find the critical number(s). d). Find the a value and the dimension of the box that will lead to the minimum total cost. e). What is the minimum cost?
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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A closed box with a square base is to have a volume of 16, 000 cm?. The material for the top and
bottom of the box cost $3 per square centimeter, while the material for the sides costs $1.50 per
square centimeter. Let x be the length of the side of the square base. a). Write an expression for
the height of the box in terms of x, b). Set up the cost C(x) as a function of x, find the domain.
c). Find C'(x), and find the critical number(s). d). Find the a value and the dimension of the box
that will lead to the minimum total cost. e). What is the minimum cost?
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