Question

The manager of a industrial plant is planning to buy a machine of either type A or type B. For
each day’s operation the number of repairs X, that the machine A needs is a poisson random
variable with mean 0.96. The daily cost of operating A is C_A = 160 + 40X²
. For machine B, let
Y be the random variable indicating the number of daily repairs, which has mean 1.12, and the
daily cost of operating B is C_B = 128 + 40Y²
. Assume that the repairs take negligible time and
each night the machine are cleaned so that they operate like new machine at the start of each
day. Which machine minimizes the expected daily cost?

Answer 1

Solution :

Let X denote the number of repairs that machine A needs.

So,

Now,

Then, expected daily cost for machine A is,

.

Let Y denote the number of repairs that machine B needs.

So,

Now,

Then, expected daily cost for machine B is,

.

So expected daily cost for machine A is 198.4 and expected daily cost for machine B is 172.8.

Thus machine B minimizes the cost.

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