Question

A closed rectangular box with a square base is to be constructed to hold 96ft^3. The material for the base costs $2 per ft^2 and the material for the top and sides costs $1 per ft^2. Find the dimensions of the box that minimizes the cost of materials.

Answer 1

Well, first define variables for the sidelengths. Then write two equations. One equation for the volume and another for the materials cost.

Answer 2

Volume: 96 = x^2y
Cost: C=3x^2+4xy

Now what?

Answer 3

IDK I'd start by solving for y in in your first equation and plugging it in cost equation.

Answer 4

But I know i have to use derivatives somehow.. trying to figure out where

Answer 5

would it be safe to assume if you maximize volume then you maximized price :)

Answer 6

minimized price lol

Answer 7

you wanna build it with the least material possible. Your box might wanna be square boxed wlh all the same.

Answer 8

Use the volume equation to write y in terms of x. Then substitute that into your cost equation.

Answer 9

That's the first step, and the result will be that you have a cost equation that only depends on x. Then you can use derivatives =)
take the derivative of the cost with respect to x. Set equal to 0 and solve to find the critical points. Evaluate the cost function at all of the critical points to find which point is the lowest.

Answer 10

if you going to use differentiation that is only to find the max..

As in if you have a function in terms of x ( f(x) )

then f'(x)=0

is the max point.

Answer 11

False, timo.
Maximums and minimums both happen when f'(x) = 0.