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A company manufactures an assembly consisting of a frame, a shaft and a ball bearing. The company manufactures all three parts on various machines of the company. Each shaft must be processed on a forging machine, a lathe and a grinder. These operations require 0.5 hours, 0.2 hours and 0.3 hours per shaft respectively. Each frame requires 0.8 hours on the forging machine, 0.1 hours on the drilling machine, 0.3 hours on the milling machine and 0.5 hours on a grinder. On the other hand, a ball bearing requires 0.7 hours, 0.4 hours and 0.3 hours on the lathe, drilling and milling machines respectively. The company has 5 lathes, 10 grinders, 20 forging machines, 3 drillers and 6 millers. Assume that each machine operates a maximum of 2400 hours per year. Formulate the LP of finding the maximum production output from the machines given that an assembly consists of two frames, a shaft and three ball bearings.
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