4. Bubble tea machine in the local shop can be either working or broken on a given day. If it is working, it could break down by the end of the day with probability of 0.03. If does break down, the owner will spend the next day fixing it and will be successful with probability of 0.9 and the machine will back in service the next morning. If the machine is not fixed at the end of the day, the owner will keep working to fix the machine the following day; the probability of getting the machine fixed on the following day is the same as on the first broken day. If the machine is not fixed at the end of the second repair day, a new machine at a cost of $5,000 will be shipped overnight and put into service the next morning. Assume that a new machine has the same probability of breaking down as a used machine. It costs $500/day for the owner to close the shop and work on bubble tea machine. a. Describe the steady state behavior of the bubble tea machine? b. What is the expected cost of running the bubble tea machine per day? c. Why would one replace the machine after the second day of downtime at such a large cost compared to the repair cost?
4. Bubble tea machine in the local shop can be either working or broken on a given day. If it is working, it could break down by the end of the day with probability of 0.03. If does break down, the owner will spend the next day fixing it and will be successful with probability of 0.9 and the machine will back in service the next morning. If the machine is not fixed at the end of the day, the owner will keep working to fix the machine the following day; the probability of getting the machine fixed on the following day is the same as on the first broken day. If the machine is not fixed at the end of the second repair day, a new machine at a cost of $5,000 will be shipped overnight and put into service the next morning. Assume that a new machine has the same probability of breaking down as a used machine. It costs $500/day for the owner to close the shop and work on bubble tea machine. a. Describe the steady state behavior of the bubble tea machine? b. What is the expected cost of running the bubble tea machine per day? c. Why would one replace the machine after the second day of downtime at such a large cost compared to the repair cost?
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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Transcribed Image Text:4. Bubble tea machine in the local shop can be either working or broken on a given day. If it is
working, it could break down by the end of the day with probability of 0.03. If does break down,
the owner will spend the next day fixing it and will be successful with probability of 0.9 and the
machine will back in service the next morning. If the machine is not fixed at the end of the day,
the owner will keep working to fix the machine the following day; the probability of getting the
machine fixed on the following day is the same as on the first broken day. If the machine is not
fixed at the end of the second repair day, a new machine at a cost of $5,000 will be shipped
overnight and put into service the next morning. Assume that a new machine has the same
probability of breaking down as a used machine. It costs $500/day for the owner to close the shop
and work on bubble tea machine.
a. Describe the steady state behavior of the bubble tea machine?
b. What is the expected cost of running the bubble tea machine per day?
c. Why would one replace the machine after the second day of downtime at such a large cost
compared to the repair cost?
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