Orders are expected to arrive at a machining center according to Poisson process at a mean rate of

$30$ per hour. The management has an option of two machines M$1($fast but expensive$)$ and M$2$

$($slow inexpensive$).$ Both machines would have an exponential distribution for machining times with

M$1$ having a mean of $1\mathrm{.}2$ minutes and M$2$ having a mean of $1\mathrm{.}5$ minutes. The profit per year is given by

Rs$.72,\frac{000}{W},$ where $W$ is the expected waiting time $($in minutes$)$ for the orders in the system. Determine

the upper bound on the difference in the average yearly cost that would justify buying M$1$ rather than M$2.$