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The manager of an industrial plant is planning to buy a new machine of either type A
or type B. If t denotes the number of hours of daily operation, the number of daily
repairs Y1 required to maintain a machine of type A is a random variable with mean
and variance both equal to .10t. The number of daily repairs Y2 for a machine of
type B is a random variable with mean and variance both equal to .12t. The daily
cost of operating A is CA(t) = 10t + 30Y21
; for B it is CB(t) = 8t + 30Y22
. Assume
that the repairs take negligible time and that each night the machines are tuned so
that they operate essentially like new machines at the start of the next day. Which
machine minimizes the expected daily cost if a workday consists of (a) 10 hours and
(b) 20 hours?

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关键词：解题思路 Industrial Essential operating ndustrial industrial operation maintain planning required

Let me see see.

What are Y22 and Y21?

Oh, they actually are Y1^2 and Y2^2. E[Yi^2] equals (EYi)^2 + Var(Yi), for i = 1,2. Therefore, E(Y1^2) = 0.1t + 0.01t^2, E(Y2^2) = 0.12 t + 0.0144t^2. Thus you get E[CA] and E[CB], based on which you substitute the value of t for each condition. And you compare to get the results.