The Euro Watch Company assembles expensive wristwatches and then sells them to retailers throughout Europe. The watches are assembled at a plant with two assembly lines. These lines are intended to be identical, but line 1 uses somewhat older equipment than line 2 and is typically less reliable. Historical data have shown that each watch coming off line 1, independently of the others, is free of defects with probability 0.98.The similar probability for line 2 is 0.99. Each line produces 500 watches per hour. The production manager has asked you to answer the following questions.
1. She wants to know how many defect-free watches each line is likely to produce in a given hour. Specifically, find the smallest integer k (for each line separately) such that you can be 99% sure that the line will not produce more than k defective watches in a given hour.
2. Euro Watch currently has an order for 500 watches from an important customer. The company plans to fill this order by packing slightly more than 500 watches, all from line 2, and sending this package off to the customer. Obviously, Euro Watch wants to send as few watches as possible, but it wants to be 99% sure that when the customer opens the package, there are at least 500 defect-free watches. How many watches should be packed?
3. Euro Watch has another order for 1000 watches. Now it plans to fill this order by packing slightly more than one hour’s production from each line. This package will contain the same number of watches from each line. As in the previous question, Euro Watch wants to send as few watches as possible, but it again wants to be 99% sure that when the customer opens the package, there are at least 1000 defect-free watches.
The question of how many watches to pack is unfortunately quite difficult because the total number of defect-free watches is not binomially distributed.(Why not?) Therefore, the manager asks you to solve the problem with simulation (and some trial and error).
4. Finally, Euro Watch has a third order for 100 watches. The customer has agreed to pay $50,000 for the order—that is, $500 per watch. If Euro Watch sends more than 100 watches to the customer, its revenue doesn’t increase; it can never exceed $50,000. Its unit cost of producing a watch is $450, regardless of which line it is assembled on. The order will be filled entirely from a single line, and Euro Watch plans to send slightly more than 100 watches to the customer. If the customer opens the shipment and finds that there are fewer than 100 defect-free watches, then he will pay only for the defect-free watches—Euro Watch’s revenue will decrease by $500 per watch short of the 100 required—and on top of this, Euro Watch will be required to make up the difference at an expedited cost of $1000 per watch. The customer won’t pay a dime for these expedited watches.
You have been asked to develop a spreadsheet model to find Euro Watch’s expected profit for any number of watches it sends to the customer. You should develop it so that it responds correctly, regardless of which assembly line is used to fill the order and what the shipment quantity is.