Patrick would like to construct a box with volume of exactly 45ft^3 using only metal and wood. The metal costs $14/ft^2 and the wood costs $5/ft^2. If the wood is to go on the sides, the metal is to go on the top and bottom, and if the length of the base is to be 3 times the width of the base, find the dimensions of the box that will minimize the cost of construction. Round answer to two decimal places.
v = w*3w*h = 45
h = 15/w^2
The cost c is
c = 14*2(w*3w) + 5*2(wh+3wh)
= 84w^2 + 300/w
So now find where dc/dw = 0 and finish it off