$3.$ A company that operates for $50$ weeks in a year is concerned about its stocks of copper cable. This costs RS $240$ a meter and there is a demand for $8000$ meters a week. Each replenishment costs Rs $1050$ for administration and Rs $1650$ for delivery, while holding costs are estimated at $25\%$ of the value held a year. Assuming no shortages are allowed,

a$)$ What is the optimal lot size for the company? $(6$ marks$)$

b$)$ Also calculate total inventory cost $(6$ marks$)$

c$)$ Assuming a safety stock of $2000$ meters, find the inventory turnover. $(8$ marks$)$