ou are the Chief Manufacturing Systems Engineer for the Tech Potato Chip and Semiconductor Chip Company. ("We strive for

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ou are the Chief Manufacturing Systems Engineer for the TechPotato Chip and Semiconductor Chip Company. ("We strive forexibility.") You have been asked to design the production line fortheir newest product, which combines the best features of boththeir product lines in a single convenient package.
Recommend the cheapest configuration of a two-machinedeterministic processing time production line. They can run theline at a speed of 1 part per minute or 2 parts per minute. Thatis, both machines can have an operation time of 1 minute or 30seconds.
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 inunits of events per minute.
If we want to run the line at 1 part per minute, we have achoice 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 forthe second machine, and its parameters are (r; p) = (.01, .006) andits cost is $20,000.
If we run it at 2 parts per minute, we have a choice of twomodels for the rst machine: (a) one with (r; p) = (.005, .009) anda cost of $20,000; and (b) one with (r; p) = (.005, .007) and acost of $30,000. There is only one model available for the secondmachine, and its parameters are (r; p) = (.005, .007) and its costis $30,000.
Here, we interpret optimal as meaning that the system is able tomeet the specified demand rate, and the sum of capital cost (thecost of the machines) and inventory cost is minimized. For thispurpose, consider the inventory cost as simply the dollar value ofthe average buffer level.
What is the optimal buffer size if inventory costs $50 each?
Regardless of line speed.
What is the cost of the optimal line if inventory costs $70each?
What is the cost of the optinal line if inventory costs $400each?