Question

Restriction help!!

A box with a square base and no top must have a volume of 10000cm^3. Determine the dimensions of the box that minimize the amount of materials used. The smallest dimension possible is 5cm

What is the restriction in here? I already found the answer h = 13.6 and w=l = 27.1
but dont know what is the restrictions

Answer 1

@mathteacher1729

Answer 2

restriction is \(w^2h=3000\)

Answer 3

where is that 3000 from??
first I thought is 100 because 100x1000 gives 10000 (so cant have any volume)
but when i plug it into the surface area equation, it gives a huge number..

Answer 4

These notes might help:
http://tutorial.math.lamar.edu/Classes/CalcI/Optimization.aspx
http://tutorial.math.lamar.edu/Classes/CalcI/MoreOptimization.aspx
and
http://www.math.ucdavis.edu/~kouba/CalcOneDIRECTORY/maxmindirectory/MaxMin.html

Answer 5

oh because i wasn't paying attention doh
should have been \(w^2h=1000\)

Answer 6

can u tell me how to get it...kinda confuse

Answer 7

you are given that the volume is fixed, that is it must be 1000 square whatever
and the base is a square with area \(w^2\) assuming you are using "w" as the variable representing the lenght of the base, and the height is "h" if you use that variable for height
volume is therefore \(w^2h\) area of the base times the height.

Answer 8

The very first problem on this page is almost identical to your original problem. :)

http://www.cliffsnotes.com/study_guide/Maximum-Minimum-Problems.topicArticleId-39909,articleId-39895.html

Answer 9

The equation I have is
S = x^2 + 40000/x
(when i combine the 2 equations together)

so if i plug in x = 1000 , then i get 1000040 for surface area
so doesnt seem restricted?

Answer 10

oh really, i will take a look at it! thks mathteacher

Answer 11

so you have two representations for the volume, one in terms of variables \(w^2h\) and the other a number you know, namely 10000, giving
\[w^2h=1000\]

Answer 12

isnt it w^2h = 10000

Answer 13

@mathteacher1729 but that question only shows the min value, but not the restrictions

Answer 14

restriction is first line
\[x^2h=100\]

Answer 15

or rather
\[x^2h=1000\]