You're selling pairs of shoes for $$90$ a pair at a fairly steady rate of $8$ pairs per week. An order of q pairs of shoes costs $20+40q$ dollars and takes $2$ week to arrive. Managing

inventory costs $$0\mathrm{.}22$ per pair of shoes per week. Under the optimal inventory control policy, you place an order for $Q$ pairs of shoes, then after you have sold $m$ of those $Q$ pairs

of shoes you submit a new order; the new shoes will arrive when you have sold out of the final $Q-m$ pairs of shoes. Find $m.$

Round your answer to the nearest whole number.

$2,893$