Optimization Nightmare

A 55-gallon Tight Head Steel Drum is constructed by attaching 18 gage (i.e. .0428 inches thick) steel disks to the top and bottom of a cylinder created by rolling up a 20 gage (i.e. .0324 inches thick) steel sheet. The vertical seam on the cylinder is welded together and the top and bottom are attached by a pressing/sealing machine. The pressing/sealing process requires approximately 13/16 inches from the top and bottom cylinder and 3/4 inches from the edge of the disk to be curled together and hence these inches are lost in the final dimensions. In addition, the top and bottom are set down 5/8 inches into the cylinder to allow a lip to the drum for ease of movement. The exterior has a height of 34.5 inches and the interior has a diameter of 22.5 inches. Steel can be purchased in coils (rolls) of any specified width so here are the costs- 18 gauge steel is 68 cents/square foot, 20 gauge steel is 51 cents/square foot, welding and pressing/sealing costs 15 cents per foot, and cutting steel costs 3 cents per foot. Compute cost of the drum specified.