Optimization Problem:

The rectangular enclosure for a loudspeaker system is to have an internal volume of 2.4ft^3. For aesthetic reasons the height of the enclosure is to be 1.5 times its width. If the top, bottom, and sides of the enclosure are to be constructed of veneer costing 80 cents per square foot and the front and rear are to be constructed of particle board costing 40 cents per square foot, find the dimensions of the enclosure that can be constructed at a minimum.

Question

Optimization Problem:

The rectangular enclosure for a loudspeaker system is to have an internal volume of 2.4ft^3. For aesthetic reasons the height of the enclosure is to be 1.5 times its width.  If the top, bottom, and sides of the enclosure are to be constructed of veneer costing 80 cents per square foot and the front and rear are to be constructed of particle board costing 40 cents per square foot, find the dimensions of the enclosure that can be constructed at a minimum.

anonymous · Answer

So I expressed everything in terms of w
V = 2.4ft^3
V = lwh
h = 1.5w
l = 2.4/(1.5w^2)
w is just w

My cost function is
(0.8)(2lw + 2wh) + (0.4)(2lh)

Did I do something wrong here?