A machine shop processes two types of parts that both involve three consecutive steps: (1) polishing, (2) drilling, and (3) tapping. These steps are performed by three machine tools that each has 5%, 10% and 20% down time respectively. Besides, the defective rates of the three steps are α=1%, β=5% and γ=5% respectively. Product A requires 5 min of polishing, 2 min of drilling, and 2 min of tapping. Product B requires 2 min of polishing, 5 min of drilling and 3 min of tapping. The total work time of polishing and drilling and tapping are all 2400 minutes per week. If the unit net profit of product A and B are $5 and $3 each. Formulate a linear programming problem that help you to decide the number of products A and products B to process in one week.