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$.$

$315\mathrm{.}7$What is the annual ordering cost if the optimal ordering quantity is used?$$

a$.$

$1071\mathrm{.}4$

b$.$

$1146$

c$.$

$1355\mathrm{.}2$

d$.$

$1515\mathrm{.}4$What is the total annual cost if the optimal ordering quantity is used?

a$.$

$126315\mathrm{.}4$

b$.$

$127830\mathrm{.}7$

c$.$

$129922\mathrm{.}1$

d$.$

$126550$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$.$

$2600$

b$.$

$414\mathrm{.}0$

c$.$

$184\mathrm{.}0$

d$.$

$92\mathrm{.}0$What is the total annual cost with the discount?

a$.$

$137464\mathrm{.}0$

b$.$

$143184\mathrm{.}0$

c$.$

$143704$

d$.$

$131744\mathrm{.}0$