Hey guys. I have a problem due tomorrow for calculus class that is very difficult for me. To be honest I have no idea where to begin. The only thing I know is that the relevant information comes near the end of the problem. Any help would be greatly appreciated.

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 -1^3 i•n ches from the cylinder and J inches from 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 r inches into the cylinder. For clarification, refer to the American National Standard (ANSI) specification diagram below.

Steel can be purchased in coils (rolls) of any specified width. Construction costs can besummarized as follows:

18 gage steel is 45 cents/square foot

20 gage steel is 34 cents/square foot

welding and pressing/sealing cost 10 cents/foot

cutting steel costs 2 cents/foot.

Is the ANSI specified drum the most efficient use of material in order to obtain the required 57.20 gallon minimum volume capacity of a 55 gallon drum? Fully justify your answer.