Log iv??? MATHEMATICAL ASSOCIATION OF AMERICA webwork / math256spring18section2/

Question

Log iv??? MATHEMATICAL ASSOCIATION OF AMERICA webwork / math256spring18section2/14.7/10 ts 14.7: Problem 10 10 Previous Problem Prodlem Lst Next Problem List Next Problem (1 point) You are to manufacture a rectangular box with 3 dimensions x, y and z, and volume v 8. Find the dimensions which minimize the surface area of this box Note: You can earn partial credit on this problem. You have attempted this problem 0 times. You have unlimited attempts remaining Page generated at 03/27/2018 at 06:53pm EDT WeBWork O 1996-2017 theme: math4 | ww_version:

Explanation / Answer

Given volume is 8, hence

xyz =8

z = 8/(xy)

Find surface area as

S = 2xy+2yz +2zx

S = 2xy+2y*(8/(xy)) +2*(8/(xy))x

S =2xy +16/x +16/y

Find partial derivative as

Sx= 2y -16/x²

Sy= 2x -16/y²

To find critical point, solve Sx=0 and Sy=0

2y -16/x² = 0

2x -16/y² =0

hence

x =y =2

then

z= 8/(2*2) =2

Thus,

x =2

y=2

z =2

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