K i got this application question the other day in my introduction to calculus class and i was wondering if anyone could lend me a hand.

Katie is building a wooden rectangular storage box. The box will have an open top and a volume of 1.5m cubed. For design purposes, Katie would like the length of its base to be triple its width. Thick wood for the base costs $8/m squared and thinner wood for the sides costs $5/m squared.

a) Express the cost of the wood as a finction of the width of the base.

b) Find all possible dimensions if Katie spends $44 for the wood.

c) what dimensions would you recommend? Why?

Now, i think if someone could help me with a) then i probably would be able to get the rest. I have figured out the base of the box is 3w + w, where w represents the the width size, but given that i do not know how to get the height of the box. I believe if i can determine the w variable then i could find the height by manipulating the formula for the volume of a box (V= lwh). anyways any help would be greatly appreciated..