Pagliacci Pizzahas designed a cardboard delivery box from a single piece of cardboard, as pictured.

(a) Find a polynomial functionv(x)

that computes the volume of the box in terms ofx.

(b) Find a polynomial functiona(x)

that computes theexposedsurface area of the closed box in terms ofx.

(c) What are the explicit dimensions if theexposedsurface 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)=2x^{3}-120x^{2}+500x = x^{3}-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:

length= 2(20-2x)

width= 2(25-2x)

height=x

plug into:

surface area of a box: 2lw+ 2lh+ 2wh???

therefore for (c) I do not know what to set equal to 600