(a) A jewelry box is constructed by partitioning a box with a squarebase as shown in the accompanying figure. If the box is designedto have volume 1,152 cm³, express the total surface area (top,bottom, sides, and interior partitions) as a function of x and y.Ignore the thickness of the material. Use the method of Lagrangemultipliers to identify the dimensions that will minimize its totalsurface area. Notice that we have said nothing about where thepartitions are located. Does it matter?Top viewx(b) Suppose the jewelry box in (a) is designed so that the material inthe top costs twice as much as the material in the bottom and sidesand three times as much as the material in the interior partitions.If the material in the interior costs $2 per cm², express the totalcost of constructing the box as a function of x and y. Use themethod of Lagrange multipliers to identify the dimensions thatwill minimize the total cost of constructing the box. What is theminimum total cost?

This is a problem of optimization.

A jewelry box is constructed by partitioning a box with a square base as shown in the accompanying figure. If the box is designed to have volume 1,152 cm³, express the total surface area (top, bottom, sides, and interior partitions) as a function of x and y. Ignore the thickness of the material. Use the method of Lagrange multipliers to identify the dimensions that will minimize its total surface area. Notice that we have said nothing about where the partitions are located. Does it matter? Top view Suppose the jewelry box in (a) is designed so that the material in the top costs twice as much as the material in the bottom and sides and three times as much as the material in the interior partitions. If the material in the interior costs $2 per cm², express the total cost of constructing the box as a function of x and y. Use the method of Lagrange multipliers to identify the dimensions that will minimize the total cost of constructing the box. What is the minimum total cost?

A jewelry box is constructed by partitioning a box with a square base as shown in the accompanying figure. If the box is designed to have volume 1,152 cm³, express the total surface area (top, bottom, sides, and interior partitions) as a function of x and y. Ignore the thickness of the material. Use the method of Lagrange multipliers to identify the dimensions that will minimize its total surface area. Notice that we have said nothing about where the partitions are located. Does it matter? Top view Suppose the jewelry box in (a) is designed so that the material in the top costs twice as much as the material in the bottom and sides and three times as much as the material in the interior partitions. If the material in the interior costs $2 per cm², express the total cost of constructing the box as a function of x and y. Use the method of Lagrange multipliers to identify the dimensions that will minimize the total cost of constructing the box. What is the minimum total cost?

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter7: Analytic Trigonometry

Section7.6: The Inverse Trigonometric Functions

Problem 92E

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