$($b$)$ An electric company which generates and distributes electricity conducted a study

on the life of poles. The repatriate life data are given in the following table:

Life data of electric poles

If the company now installs $5,000$ poles and follows a policy of replacing poles only

when they fail, how many poles are expected to be replaced each year during the

next ten years?

To simplify the computation assume that failures occur and replacements are made

only at the end of a year.

If the cost of replacing individually is $160$ per pole and if we have a common group

replacement policy it costs $80$ per pole, find out the optimal period for group