Bata Shoe can produce $10,000$ pairs of shoes per day. However, its management believes that the effective capacity is $90\%.$ Currently, the company is producing $8,500$ pairs of shoes per day.

$($a$)$ Calculate utilization $(5$ marks$)$

$($b$)$ Calculate efficiency $(5$ marks$)$

$($c$)$ The company has decided to increase its capacity by introducing a new production line. The efficiency of the new production line is $90\%.$ Calculate the expected output of this new line.