Question

A manufacturer wants to design an open box with a square base and a surface area of 108in(squared). What dimensions will max volume? max volume?

Answer 1

each side is 54 i think becuase 108/2...i got that from A=BH

Answer 2

its surface area.. not area of the box.

Answer 3

wait is that 108 from one side?

Answer 4

oh its the...i got it..lol

Answer 5

:D

Answer 6

Yay jimmy :) REP!

Answer 7

Yes please HELP ! :) diarmuid ! and JIMMMY !

Answer 8

the maximum area of a rectangle is a square
so as there are 5 square sides each will have area 108/5 = 21.6 and side sqrt 21.6
so maxm volume will be (sqrt21.6)^3

Answer 9

no. only base is a square .. the sides are not

Answer 10

sides have to be square also maximum volume = 100.4 cu ins

Answer 11

you cant have rectangle sides and a square base

Answer 12

height of the sides are not the same as "x" when x is the length and width of the base

Answer 13

Got it thanks guys !

Answer 14

x is the base
y is the height
so 108 = x^2 + 4 xy
implies y = (-x^2 +108)/4x
also maximise yx^2 (volume)
substitue y so formula becomes (-x^3)/(4 +27x)
so max (-x^3)/4 +27x
draw for sanity ant it has a local max at x = +6 or so
differentiate
-3/4x^2 +27 = 0
so x = +-6
x = +6
108 = x^2 +4xy
72 = 4(6)y
72/24 = y
y = 3
so box dimensions are 6*6*3

Answer 15

AWESOME !

Answer 16

No worries. Is this a college question?

Answer 17

yup - good answer - i must have had a mental block on this one!