Case Study

EuroWatch 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. EuroWatch 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, EuroWatch 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. EuroWatch has another order for 1000 watches. Now it plans to fill this order by packing slightly more than one hours production from each line. This package will contain the same number of watches from each line. As in the previous question, EuroWatch 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 notbinomially distributed. (Why not?) Therefore, the manager asks you to solve the problem with simulation (and some trial and error). (Hint: It turns out that it is much faster to simulate small numbers than large numbers, so simulate the number of watches with defects, not the number without defects.)
4. Finally, EuroWatch has a third order for 100 watches. The customer has agreed to pay $50,000 for the orderthat is, $500 per watch. If EuroWatch sends more than 100 watches to the customer, its revenue doesnt 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 EuroWatch plans to send slightly more than 100 watches to the customer.
5. If the customer opens the shipment and finds that there are fewer than 100 defect-free watches (which we assume the customer has the ability to do), then he will pay only for the defect-free watchesEuroWatchs revenue will decrease by $500 per watch short of the 100 requiredand on top of this, EuroWatch will be required to make up the difference at an expedited cost of $1000 per watch. The customer wont pay a dime for these expedited watches. (If expediting is required, EuroWatch will make sure that the expedited watches are defect-free. It doesnt want to lose this customer entirely.)
6. You have been asked to develop a spreadsheet model to find EuroWatchs 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. (Hints: Use the BINOM.DIST function, with last argument 0, to fill up a column of probabilities for each possible number of defective watches. Next to each of these, calculate EuroWatchs profit. Then use a SUMPRODUCT to obtain the expected profit. Finally, you can assume that EuroWatch will never send more than 110 watches. It turns out that this large a shipment is not even close to optimal.)

Each case study must be of original discussion and analysis, not counting the title page, reference page, figures, tables, and appendixes. The statements in each Case Study must be supported by biblicalintegration and at least 2 scholarly references, cited throughout the narrative and placed on the reference list in the APA format. Case Study assigned questions are listed in the chart below.

Note: Your assignment will be checked for originality via the Turnitin plagiarism tool. The tool is a starting point for instructors to check overall Academic Integrity and higher scores generally indicate a higher probability of Academic Misconduct. The higher a score the higher the probability that there are too high a percentage of quotations included in the narrative, and/or there are passages that have not been properly cited.