Question

A manufacturer wants to design an open top box having square base and a surface area of 48 square inches. What dimensions will produce a box with maximum volume?
The height of the box should be inches,
and the base of the box should be × inches.

Answer 1

s=48 s=x^2+4xh
V=x^2h

Answer 2

so 48=x^2+4xh

Answer 3

it's probably easier to solve for h in 48=x^2+4xh

Answer 4

then plug this into V=x^2h

then derive to find the critical values, which will lead you to the max volume (with corresponding dimensions)

Answer 5

so 48/(x^2+4x)=h

Answer 6

no

Answer 7

more like

48=x^2+4xh

48-x^2=4xh

h = (48 - x^2)/(4x)

Answer 8

ah ok my bad, been a long day lol

Answer 9

V=x^2((48 - x^2)/(4x))
V'=12-(3 x^2)/4

Answer 10

got it thanks

Answer 11

V=x^2h

V=x^2((48 - x^2)/(4x))

V = (1/4)*x(48-x^2)

V = (x^3)/4 - 12x

V ' = (3x^2)/4 - 12

0 = (3x^2)/4 - 12

solve for x

Answer 12

oh ok, glad you did

Answer 13

thanks

Answer 14

yw