You're building a rectangular box. The material for the bottom costs $0.60 per square foot, and the material for the sides and the top cost $0.20 per square foot. a) Find the dimensions to maximize the volume for such a box if the total amount of money available for material is $12. b) Find the total volume of the box. Answer with a sentence and use appropriate units. Hint: This problem works nicely using LaGrange Multipliers.
You're building a rectangular box. The material for the bottom costs $0.60 per square foot, and the material for the sides and the top cost $0.20 per square foot. a) Find the dimensions to maximize the volume for such a box if the total amount of money available for material is $12. b) Find the total volume of the box. Answer with a sentence and use appropriate units. Hint: This problem works nicely using LaGrange Multipliers.
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 37E: Zaidah plans a raised flower bed 2 ft high by 12 ft wide by 15 ft long. The mulch, soil, and peat...
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Transcribed Image Text:You're building a rectangular box. The material for the bottom costs $0.60 per
square foot, and the material for the sides and the top cost $0.20 per square foot.
a) Find the dimensions to maximize the volume for such a box if the total
amount of money available for material is $12.
b) Find the total volume of the box.
Answer with a sentence and use appropriate units. Hint: This problem works
nicely using LaGrange Multipliers.
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