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 $$92$ and the cost per container is $$24.$ One decimal point for all calculations.

What is the optimal ordering quantity?$$

a$.$

$353\mathrm{.}0$

b$.$

$446\mathrm{.}5$

c$.$

$2600$

d$.$

$315\mathrm{.}7$