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 $$96$ and the cost per container is $$20.$ One decimal point for all calculations.

What is the optimal ordering quantity?

a$.$

$2600$

b$.$

$353\mathrm{.}3$

c$.$

$499\mathrm{.}6$

d$.$

$395\mathrm{.}0$ What is the annual ordering cost if the optimal ordering quantity is used?

a$.$

$999\mathrm{.}2$

b$.$

$1068$

c$.$

$1263\mathrm{.}8$

d$.$

$1413\mathrm{.}0$ What is the total annual cost if the optimal ordering quantity is used?

a$.$

$108777\mathrm{.}0$

b$.$

$105632$

c$.$

$106825\mathrm{.}9$

d$.$

$105413\mathrm{.}0$ The supplier offers a $$1$ per unit discount if the order is for $6$ months worth of the demand $(2,600$ units$).$ What is the annual ordering cost in this case?

a$.$

$432\mathrm{.}0$

b$.$

$2600$

c$.$

$96\mathrm{.}0$

d$.$

$192\mathrm{.}0$ What is the total annual cost with the discount?

a$.$

$118752$

b$.$

$120312\mathrm{.}0$

c$.$

$114592\mathrm{.}0$

d$.$

$108872\mathrm{.}0$