2. [30 points] The plastic bottle plant requires 7 operations to produce the bottle. They found that the first step of the operations is a bottleneck resource. The company wants to know the number of machines they need for the first step of the operations to release the bottleneck; this information assists for the plant to decide how many additional machines they need to purchase. The plant produces 3,000,000 good quality bottles annually and operates three 8-hr shift for 250 days/yr. The plant produces 10,000 good bottles per batch. The scrap rate is 7%. On average, it takes 55 sec to produce each bottle when the machine is running. Before each batch, the machine needs to be set up, which takes 3 hr per setup. The availability of the machines is 88% during the production and 100% during setup. Determine (a) Total number of machines required to accomplish the specified production [25 points] (b) If the plant has currently 6 machines, how many machines would you suggest for the plant to purchase? [5 points]