Minimisation Question (1 Viewer)

rama_v

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Hey everyone, Can I please get help with this question:

An open box is to be made of thin sheet metal with a square base having edges x metres long and vertical sides y metres long. It is to have a volume of 2 m3
(i) Show that the surface area of the box (asuming negligible thickness) is given by A = (8/x) + x2

k I got that part..the next part though I can't.

(ii) Prove that the cost of insulating the inside of the box will be a minimum if x =2y
 

Jago

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from (i)
x² = 2 / y

A = x² + 8/x
A' = 2x - 8/x²
2x = 8y/2 = 4y
x = 2y

f"(2y) > 0

.'. min. at x = 2y blah blah blah
 

Jago

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just returning the favour
 

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