If 1900 square centimeters of material is available to make a box with a square base and an open top, find the

Question

This is on my calculus test tomorrow morning and our teacher will not explain how to do it. All he will tell us is that Area(1900)=2w^2+4hw and volume=w^2h. . . can anyone please help?

Answer 1

I assume that you want to maximize the volume.

The key here is that you can express 'h' in terms of 'w'. You know that:

1900 = w^2 + 4hw (the 2w^2 is wrong -- since the top is open).

You can rewrite this as:

h = (1900-w^2)/4w.

Now, substitute this into

V = h*w^2 to get

V =[ (1900-w^2)/4w]*w^2

Simoplify the expression on the right using algebra. Next, take the first derivative of V with respect to w. Set it equal to zero, solving for w & test to see if it is a maximum.