You have to design an open-top box (box that has a bottom and all four sides but no lid) to be made out of two different types of material. The material for the sides costs $4 per square inch. The material to make the bottom costs $3 per square inch. The bottom of the box should be a square and the volume of the box must be 3 cubic inches. Find the dimensions of the box such that the cost is minimized. Recall that the volume of a box is length x width x height.

Elementary Geometry For College Students, 7e
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ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
Chapter8: Areas Of Polygons And Circles
Section8.5: More Area Relationships In The Circle
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You have to design an open-top box (box that has a bottom and all four sides but no lid) to be made out of
two different types of material. The material for the sides costs $4 per square inch. The material to make the
bottom costs $3 per square inch. The bottom of the box should be a square and the volume of the box must
be 3 cubic inches. Find the dimensions of the box such that the cost is minimized. Recall that the volume of
a box is length x width x height.
Transcribed Image Text:You have to design an open-top box (box that has a bottom and all four sides but no lid) to be made out of two different types of material. The material for the sides costs $4 per square inch. The material to make the bottom costs $3 per square inch. The bottom of the box should be a square and the volume of the box must be 3 cubic inches. Find the dimensions of the box such that the cost is minimized. Recall that the volume of a box is length x width x height.
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