: A mining company routinely replaces a specific part on a certain type of equipment. The usage rate is forty per week, and there is no significant seasonality. The supplier of the part offers the following all$-$units discount structure.

Range Q Unit cost

$0<$ Q $<300$ units $$10\mathrm{.}00$

Q $>=300$ $$9\mathrm{.}7$

The fixed cost of a replenishment is estimated to be $$25,$ and a carrying charge of $0\mathrm{.}26$ $$/$$$/$yr$.$ is used by the company.

a$.$ What replenishment size should be used?