Two rectangular boxes side-by-side provides a top and a bottom width (w) and three side heights (h). The area of the combined boxes is….h*w

We know that 3*h + 2*w = 200, and

h * w = A

We want Amax, which will require a derivative, but we can’t do a derivative with two variables, so let’s simplify 3*h + 2*w = 200 for w and substitute it into h * w = A:

3*h + 2*w = 200

2*w = 200 – 3*h

w = 100 – 3*h/2

Substitute into l * w = A:

h * (100 – 3*h/2) = A

100*h -3*(h^2)/2 = A(h)

The maximum of A(h) can be found where the derivative of A(h) with respect to h, or d[A(h)]/dh = 0. And

d[A(h)]/dh = 100 – 3*h (assuming you can do derivatives)

So the value for h where 100 – 3*h = 0 will provide the maximum A.

100 – 3*h = 0

3*h = 100

h = 33.33333

Using 3*h + 2*w = 200, we can determine w and find the area.

3*33.333 + 2*w = 200

100 + 2*w = 200

2*w = 100

w = 50

Amax = h * w (for our derived values)

Amax = 33.333 * 50

Amax = 1666.67 meters squared