2. The manager of an industrial plant is planning to buy a new machine of either type A or B. For each day's operation, the number of repairs "X" that machine A requires is a Poisson random variable with mean 0.10t, where t denotes the time (in hours) of daily operation. The number of daily repairs "Y" for machine B is a Poisson random variable with mean 0.12t. The daily cost of operating A is C,(t) = 10t + 30X²; for B the cost is Cg(t) = 8t + 30Y². Assume that the repairs take negligible time and that the machines are to be cleaned each night so they operate like new machines at the start of each day. Which machine minimizes the expected daily cost if a day consists of (a) 10 hours? (b) 20 hours?

2. The manager of an industrial plant is planning to buy a new machine of either type A or B. For each day's operation, the number of repairs "X" that machine A requires is a Poisson random variable with mean 0.10t, where t denotes the time (in hours) of daily operation. The number of daily repairs "Y" for machine B is a Poisson random variable with mean 0.12t. The daily cost of operating A is C,(t) = 10t + 30X²; for B the cost is Cg(t) = 8t + 30Y². Assume that the repairs take negligible time and that the machines are to be cleaned each night so they operate like new machines at the start of each day. Which machine minimizes the expected daily cost if a day consists of (a) 10 hours? (b) 20 hours?

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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Estimation

A new framework of data analysis where the new statistical methods are used for interpreting the results and analyzing the data is known as estimation in statistics.

Question

2. The manager of an industrial plant is planning to buy a new machine of either
type A or B. For each day's operation, the number of repairs "X" that machine A
requires is a Poisson random variable with mean 0.10t, where t denotes the time (in
hours) of daily operation. The number of daily repairs "Y" for machine B is a Poisson
random variable with mean 0.12t. The daily cost of operating A is C,(t) = 10t + 30X²;
for B the cost is C3(t) = 8t + 30Y². Assume that the repairs take negligible time and
that the machines are to be cleaned each night so they operate like new machines
at the start of each day. Which machine minimizes the expected daily cost if a day
consists of (a) 10 hours? (b) 20 hours?

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