Question 1:

Suppose you are a production manager for a small firm that manufactures GPUs (i.e., video cards) for computers. Your production facility utilizes three identical machines. Quality is binary each GPU is either defective or it is not defective. Machine 1 produces 40 GPUs per day, and past experience suggests that, on average, 1% of its output will be defective. Machine 2 produces 20 GPUs per day, and past experience suggests that, on average, 3% of its output will be defective. Machine 3 produces 10 GPUs per day, and past experience suggests that 4% of its output will be defective. Any unit of output is not identifiable as having been produced by Machine 1, 2 or 3. On April 7, 2021, post-production quality inspection of the day's output of 70 GPUs revealed that 6 were defective. This could happen by chance. But if the firm assesses the probability of this happening to be 5% or less, its policy is to have one or more of its machines serviced. What should the firm do?

Question 2:

You are the Materials Manager at a local hospital. Your job is to ensure that the hospital has a sufficient supply of protective masks for medical staff who are involved in the examination and testing of suspected COVID-19 cases. Each suspected case (i.e., patient) is examined and tested by a single nurse. With each new patient, the nurse must wear a new mask. On May 1, you expect the number of suspected cases to follow a Poisson distribution with a mean of 20. Each day thereafter, the expected (i.e., mean) number of suspected cases is forecast to increase by 5%. Explain in detail how you would decide how many masks to order for the entire month of April (assuming that masks are available).

Question 3:

Explain in detail how regression analysis can be utilized to forecast the demand for a firm's output