The manager of an industrial plant is planning to buy a new machine of either ty
ID: 2924795 • Letter: T
Question
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+30(Y1)^2; for B it is CB(t) = 8t+30(Y2)^2. Assume that the repairs take negligible time and that each night the machines are tuned so that they operate essentially like new at the start of the next day. Which machine minimizes the expected daily cost if a workday consists of a)10 hours,b)12 hours?
Explanation / Answer
The expected daily cost for A:
Var(Y1)=E[Y1^2]-E[Y1]^2 t
E(CA(t)) = E[10t + 30Y12 ] = 10t + 30E(Y12)
= 10t + 30 { V (Y1) + [E(Y1) }
= 10t + 30[0.10t + (.10t2)
=13t + 0.3t2
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