A rectangular packing box, similar to a shoebox, without a lid, is 3 times as long as it is wide and half as high as it is long. Each square inch of the bottom of the box costs $0.008 to produce, while each square inch of any side costs $0.003 to produce.

(A) Write an equation that represents the cost, c, of the box as a function of its width x.

(B) Using the function written in part a, determine the dimensions of a box that would cost $0.69 to produce.