$3$ Working with the $(Q,R)$ Model

A local paint store uses a $(Q,R)$ inventory system to control its stock levels. For a popular eggshell indoor paint, historical data shows the distribution of annual demand is approximately normal, with a mean of $468$ cans and variance of $1872,$ expressed as $N(468,1872).$ Replenishment lead time for this paint is about $14$ weeks. Each can of paint costs the store $$6.$ The fixed cost of replenishment is $$45$ per order and holding costs are based on a $20\%$ annual interest rate.

What is the holding cost $h?$

a$.$ $$1\mathrm{.}20$

b$.$ $$7\mathrm{.}80$

c$.523\mathrm{.}60$

d$.$ $$15\mathrm{.}40$

What is the optimal order quantity $Q^{**}($also called the EOQ$)?$

a$.188$ cans per order

b$.53$ cans per order

c$.124$ cans per order

d$.22$ cans per order

What is the annual inventory cost IC under the EOQ?

$3.$ $$429\mathrm{.}16$

b$.$ $$805\mathrm{.}46$

c $$224\mathrm{.}82$

d$.$ $$653\mathrm{.}44$