Demand for Container X$-100$ is $100$ per week. There are $52$ weeks per year. The lead time to get new containers is $3$ weeks. The interest rate $($holding cost rate$)$ is $40\%.$ The cost per order is $$67$ and the cost per container is $$27.$ One decimal point for all calculations.

What is the optimal ordering quantity?

a$.$

$359\mathrm{.}2$

b$.$

$284\mathrm{.}0$

c$.$

$254\mathrm{.}0$

d$.$

$2600$