A gasoline dealer commissioned a machine shop owner to fabricate a metal tank in the shape of a cylinder of height (H) with hemispherical bottom and a circular cover. The circular top, cylinder and hemispherical bottom shall all have the same diameter (D). Cost of materials is USD 1200/m2 and labor cost is given by the equation: USD [2500/(D2H) + 3000/(DH2 )]. Find the optimum Diameter and Height.

A gasoline dealer commissioned a machine shop owner to fabricate a metal tank in the shape of a cylinder of height (H) with hemispherical bottom and a circular cover. The circular top, cylinder and hemispherical bottom shall all have the same diameter (D). Cost of materials is USD 1200/m2 and labor cost is given by the equation: USD [2500/(D2H) + 3000/(DH2 )]. Find the optimum Diameter and Height.

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 27E: The box with dimensions indicated is to be constructed of materials that cost 1 cent per square inch...

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Question

A gasoline dealer commissioned a machine shop owner
to fabricate a metal tank in the shape of a cylinder of
height (H) with hemispherical bottom and a circular
cover. The circular top, cylinder and hemispherical
bottom shall all have the same diameter (D). Cost of
materials is USD 1200/m2 and labor cost is given by the
equation: USD [2500/(D2H) + 3000/(DH2
)]. Find the optimum Diameter and Height.

Expert Solution