A vertical cylindrical steel tank of height L and inside diameter D is to be constructed. The tank is open at the top, and it is known that the bottom must be twice as thick as the side thickness, t. Determine the dimensions of the minimum cost tank of given volume V, where the total weight of the material represents the total cost of the tank. You can assume that the side thickness is negligible in determining the diameter User 2 User 1 User 3 Remainder Gage/ Allocation Site flow at gage remainder of the tank. (a) Solve the problem (find optimal values of L, D) using the Lagrange multiplier method for arbitrary V and unit cost, c. (b) Check your Lagrange multiplier solution by using Excel Solver for V = 10 m3 and a unit cost of $1.00/m2 of steel with thickness t. %3D
A vertical cylindrical steel tank of height L and inside diameter D is to be constructed. The tank is open at the top, and it is known that the bottom must be twice as thick as the side thickness, t. Determine the dimensions of the minimum cost tank of given volume V, where the total weight of the material represents the total cost of the tank. You can assume that the side thickness is negligible in determining the diameter User 2 User 1 User 3 Remainder Gage/ Allocation Site flow at gage remainder of the tank. (a) Solve the problem (find optimal values of L, D) using the Lagrange multiplier method for arbitrary V and unit cost, c. (b) Check your Lagrange multiplier solution by using Excel Solver for V = 10 m3 and a unit cost of $1.00/m2 of steel with thickness t. %3D
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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Transcribed Image Text:A vertical cylindrical steel tank of height L and
inside diameter D is to be constructed. The
tank is open at the top, and it is known that
the bottom must be twice as thick as the side
thickness, t. Determine the dimensions of the
minimum cost tank of given volume V, where
the total weight of the material represents the
total cost of the tank. You can assume that the
side thickness is negligible in determining the
diameter User 2 User 1 User 3 Remainder
Gage/ Allocation Site flow at gage remainder
of the tank.
(a) Solve the problem (find optimal values of
L, D) using the Lagrange multiplier method
for arbitrary V and unit cost, c.
(b) Check your Lagrange multiplier solution by
using Excel Solver for V = 10 m3 and a unit
cost of $1.00/m2 of steel with thickness t.
%3D
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