Question

On Paul's online math notes, in Applications of the derivative, Optimization, ex. 2, how does he go from C=10(2lw)+ 6(2wh+2lh)=60w^2+48wh??? I understand how he gets the equation, but not the answer. Thanks

Answer 1

can you provide mor einformation?

Answer 2

whats the setup to the problem, and maybe we can work thru it :)

Answer 3

Example 2 We want to construct a box whose base length is 3 times the base width. The material used to build the top and bottom cost $10/ft2 and the material used to build the sides cost $6/ft2. If the box must have a volume of 50ft3 determine the dimensions that will minimize the cost to build the box.

this one right?

Answer 4

its the cost we want to minimize....

Answer 5

l = 3w; V = lwh = 50; h = V/lw

h = 50/3ww = 50/3w^2

surface area = 2lw + 2wh + 2lh

Answer 6

cost = 2(10)lw + 2(6)wh + 2(6)lh

cost = 2(10)(3w)w + 2(6)w(50/3w^2) + 2(6)(3w)(50/3w^2)

Answer 7

cost = 60w^2 +600w/3w^2 + 1800w/w^2

cost = 60w^2 +200/w + 600/w

Answer 8

cost' = 60(2w) -800/w^2

cost' = (120w^3 -800)/w^2

cost' = 40(3w^3 -20)/w^2 = 0 when 3w^3 -20 = 0

Answer 9

3w^3 = 20

w^3 = 20/3

w = cbrt(20/3) now where if anyplace did I go wrong lol

Answer 10

w=cbrt(20/3); l=20 ; h=50/3cbrt(400/9) maybe lol

Answer 11

apparently thats correct lol...its good to have an answer key to check :)

Answer 12

This is where I get lost... cost = 2(10)lw + 2(6)wh + 2(6)lh cost = 2(10)(3w)w + 2(6)w(50/3w^2) + 2(6)(3w)(50/3w^2)

How do u got from 2(10)lw to 2(10)(3w)w?

Answer 13

length = 3 times the width in the information given; substitute 3w for l

Answer 14

I get the bottom you're replacing the h's

Answer 15

yeah; turning everything into w varaibale terms :)

Answer 16

i got cbrt(20/3) and was sure I messed it up lol....but its good

Answer 17

Oh right! But quickly, how do you solve for the height? 50/3ww?

Answer 18

V = 50 = lwh; solve for h and substitute you l value...

h = 50/lw and l = 3w

h = 50/3w^2

Answer 19

the volume of a box is (length) times (width) times (height) :)

Answer 20

ahhhh, thank you! the clouds are dispersing now! lol I'm going to try it again

Answer 21

good luck ;)