Milton Manufacturing Company, a sheet metal fabricating firm in Columbus, Ohio, produces two sizes of file cabinets; a letter size and a legal size. The letter-size cabinet sells to the distributor for $138.00, and the legal-size sells for $176.50. The cabinets are constructed from sheet metal that is ordered with a special coloring and finish. It takes 36 square feet of sheet metal to fabricate a letter-size cabinet and 54 square feet of sheet metal to complete a legal-size cabinet. Due to an unanticipated increase in demand for sheet metal from other manufacturers, Milton will not receive any new shipments until next year and has only 120,000 square feet of sheet metal to use for the remainder of the year. Fabricating cabinets requires two major operations: cutting and forming sheet metal into parts, and, subsequently assembling and welding the formed parts. The cutting and forming operations require 2 hours for a letter-size cabinet and 3 hours for a legal-size cabinet. The company has 10,000 hours of available time for this operation. Assembly and welding operations require 4 hours for a letter-size cabinet and 2 hours for the legal-size. The company has 8,000 hours of available time for this operation.
Both indirect and direct labor costs are assigned to the products manufactured by Norton. Each letter-size cabinet requires $41.00 in direct labor charges and each legal-size requires $52.00. Milton Manufacturing has allocated $375,000.00 for direct labor for the period. Milton's cost accountants have determined that the total direct and indirect costs assigned to the letter-size cabinet are $87.00 and the total direct and indirect costs allocated to the legal-size are $121.00.
I need help formulating a linear programming model that can be used to determine the production plan that will yield the maximum possible annual profit contribution for the company.