Question

Question 4: The Binomial Distribution

The company you are working for just received an order for 25 castings, made from precious metals. Each casting will sell for $5,000; however, it is also costly to produce at $2,500. Your manufacturing facility can produce castings of high quality with a probability of 0.98. All castings are produced independently.

The customer would like to receive 25 castings of high quality. However, they are willing to accept less than 25: if that happens you have to pay a penalty of $500 for each casting you are short of 25. For example, assume you only produce 23 castings of high quality: the customer will buy the 23 at the agreed upon price of $5,000 (for a total revenue of 23 ·$5, 000 = $115, 000), but you will pay a penalty of (25 ? 23)·$500 = $1, 000 (bringing your total revenue at $114,000).

Answer the following questions.

(a) Assume your company plans to produce n = 30 castings. How many castings are expected to be of high quality?

(b) How much should the company expect to make in profits from this customer (assuming they still produce n = 30 castings)?

(c) How much should the company expect to make in profits from this customer if they instead only plan to produce 25 castings?

(d) Based on your answers in (b) and (c), would you recommend they plan for 25 or 30 castings?

(e) Perform the same calculation for n = 26, 27, 28, 29. How many castings should you plan for?

Answer: For this question, you are expected to use Excel (and its BINOMDIST(x, n, p, 0) function where x=number of high quality castings, n=number of castings planned for production, p=probability of having a high quality casting produced) or SciPy (based on the notes of the class).

Answer 1

Answer: