For a specific turning operation by a cemented carbide tool insert, the Taylor's tool life equation is given by

$V{T}^{02}=152$ and the following conditions are given:

Speed range of the tool is $(80\frac{m}{m}in-100\frac{m}{m}in$

Specification of the tool insert is "SNUN $120\mathrm{.}0308"$

Cost of one tool insert is Rs$.500$

Tool tip change time is $30$ s

Cost of the blank and electricity consumed is Rs$.300$

Labor cost is Rs$.\frac{20}{m}in$

If a single tool insert is totally used for producing a single work piece at the maximum production rate,

a$)$ Estimate the total life of an insert,

b$)$ Calculate the cost of production.