A mining company routinely replaces a specific part on a certain type of equipment. The usage rate is $40$ per week and there is no significant seasonality. The supplier of the part offers the following all$-$units discount structure:

Range of Q Unit Cost

$0<$ Q $<300$ $$10\mathrm{.}00$

$300<=$ Q $$9\mathrm{.}70$

The fixed cost of a replenishment is estimated to be $$25$ and a carrying charge of $0\mathrm{.}26$ $$/$$$/$year is used by the company. If the year consists of $50$ working week:

a$.$ What replenishment size should be used?

b$.$ If the supplier was interested in having the mining company acquire at least $500$ units at a time, what is the largest unit price they could charge for an order of $500$ units