Rectangular boxes with a volume of 8 m³ are to be made of three materials. The material for the top costs $120 per m2, the bottom costs $40 per m² and the material for the sides costs $10 per m2. What are the dimensions of the box that minimizes the cost of the box? Show all work.

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
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Calculus 3

1.Solve the following question.
A. Rectangular boxes with a volume of 8 m³ are to be made of three materials. The material for the
top costs $120 per m², the bottom costs $40 per m² and the material for the sides costs $10 per m².
What are the dimensions of the box that minimizes the cost of the box? Show all work.
B. A 120 meter fence is to be cut into 3 pieces to make 3 square enclosures. How long should each
of the cut up fence pieces be in order to minimize the total area enclosed? Show all work.
C. Use the method of Lagrange Multipliers to find the dimensions of the rectangle of
maximum area with sides parallel to the coordinate axis that can be inscribed in the ellipse
4x2 +16y? = 16. Show all work.
Transcribed Image Text:1.Solve the following question. A. Rectangular boxes with a volume of 8 m³ are to be made of three materials. The material for the top costs $120 per m², the bottom costs $40 per m² and the material for the sides costs $10 per m². What are the dimensions of the box that minimizes the cost of the box? Show all work. B. A 120 meter fence is to be cut into 3 pieces to make 3 square enclosures. How long should each of the cut up fence pieces be in order to minimize the total area enclosed? Show all work. C. Use the method of Lagrange Multipliers to find the dimensions of the rectangle of maximum area with sides parallel to the coordinate axis that can be inscribed in the ellipse 4x2 +16y? = 16. Show all work.
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