A local company produces an erasable programmable read$-$only memory $($EPROM$)$ for several industrial clients. It has experienced a relatively flat demand of $3,500$ units per year for the product. The EPROM is produced at a rate of $12,000$ units per year. The accounting department has estimated that it costs $$75$ to initiate a production run, each unit costs the company $$5$ to manufacture, and the cost of holding is based on a $25$ percent annual interest rate. Determine the optimal size of a production run.

a$.$

$600$ units

b$.$

$770$ units

c$.$

$870$ units

d$.$

$540$ units