Pagliacci Pizza has designed a cardboard delivery box from a single piece of cardboard, as pictured.
(a) Find a polynomial function v(x)
that computes the volume of the box in terms of x.
(b) Find a polynomial function a(x)
that computes the exposed surface area of the closed box in terms of x.
(c) What are the explicit dimensions if the exposed surface area of the closed box is 600 sq. inches? (Round your dimensions to three decimal places. Enter your answers as a comma-separated list.)
For (a) I got, incorrectly, v(x)=2x3-120x2+500x = x3-60x+250 because, I thought, L(W)(H)
length = 20-2x
height = x
width = (50-2x)/2
For (b) I am at a complete loss.
I would guess:
surface area of a box: 2lw + 2lh + 2wh
therefore for (c) I do not know what to set equal to 600