You are the Chief Manufacturing Systems Engineer for the Tech Potato Chip and Semiconductor Chip Company. ("We strive for exibility.") You have been asked to design the production line for their newest product, which combines the best features of both their product lines in a single convenient package. Recommend the cheapest configuration of a two-machine deterministic processing time production line. They can run the line at a speed of 1 part per minute or 2 parts per minute. That is, both machines can have an operation time of 1 minute or 30 seconds. The demand on the system requires a long run production rate of .58 parts per minute. In the following, all the r's and p's are in units of events per minute. If we want to run the line at 1 part per minute, we have a choice of two models for the first machine: (a) one with (r; p) = (.01, .008) and a cost of $10,000; and (b) one with (r; p) = (.01, .006) and a cost of $20,000. There is only one model available for the second machine, and its parameters are (r; p) = (.01, .006) and its cost is $20,000. If we run it at 2 parts per minute, we have a choice of two models for the rst machine: (a) one with (r; p) = (.005, .009) and a cost of $20,000; and (b) one with (r; p) = (.005, .007) and a cost of $30,000. There is only one model available for the second machine, and its parameters are (r; p) = (.005, .007) and its cost is $30,000. Here, we interpret optimal as meaning that the system is able to meet the specified demand rate, and the sum of capital cost (the cost of the machines) and inventory cost is minimized. For this purpose, consider the inventory cost as simply the dollar value of the average buffer leve a)Assuming that both machines must operate at the same speed, what is the optimal combination of machines? M(1alpha) - M(2) M(1b) - M(2) What is the optimal buffer size if inventory costs $50 each? (Round to nearest integer) For line speed of 2 parts per minute. Assuming that both machines must operate at the same speed, what is the optimal combination of machines? What is the cost of the optimal line if inventory costs $70 each? (Round to the nearest integer) What is the cost of the optinal line if inventory costs $400 each? (Round to the nearest integer)