14. A box has a square base of side x and height y. (a) Find the dimensions x, y for which the volume is 12 and the surface area is as small as possible. (b) Find the dimensions for which the surface area is 20 and the volume is as large as possible. Hint: (a) The volume V = x²y = 12. Minimize the surface area A = 2x2 + 4xy.

14. A box has a square base of side x and height y. (a) Find the dimensions x, y for which the volume is 12 and the surface area is as small as possible. (b) Find the dimensions for which the surface area is 20 and the volume is as large as possible. Hint: (a) The volume V = x²y = 12. Minimize the surface area A = 2x2 + 4xy.

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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