A company manufactures an assembly consisting of a frame, a shaft, and a ball bearing. The company manufactures the shafts and frames but purchases the ball bearings from a ball bearing manufacturer. Each shaft must be processed on a forging machine, a lathe, and a grinder. These operations require 0.6 hour, 0.3 hour, and 0.4 hour per shaft, respectively. Each frame requires 0.8 hour on a forging machine, 0.2 hour on a drilling machine, 0.3 hour on a milling machine, and 0.6 hour on a grinder. The company has 5 lathes, 10 grinders, 20 forging machines, 3 drillers, and 6 millers. Assume that each machine operates a maximum of 4500 hours per year. Required:
Formulate the problem of finding the maximum number of assembled components that can be produced as a linear program.