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 + 40X^{2}

. 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 +
40Y^{2}

. 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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