CWD Office Supplies sells Printers, which it orders from Kajama Inc in Japan. Because of shipping and handling costs, each order must be for $5$ printers. Because of the time it takes to receive an order, the company places an order every time the present stock drops to $5$ Printers. It costs $$50$ to place an order. It costs the company $$500$ in lost sales when a customer asks for a Printer and the warehouse is out of stock. It costs $$100$ to keep each Printer stored in the warehouse. If a customer cannot purchase a Printer when it is requested, the customer will not wait until one comes in but will go to a competitor. The following probability distribution for demand for Printer has been determined: The time required to receive an order once it is placed $($lead time$)$ has the following probability distribution: We assume that no order is placed until the previous order arrives and the stock is used to the reorder level. The company has $3$ Printers in stock. Orders are always received at the beginning of the week. A lead time of $2$ weeks imply that an order placed in week one will arrive in week $4.$ Required a$)$ Construct the appropriate random number mappings for the random variables starting with $\mathrm{.}00.(2\mathrm{.}5$ marks for demand and $1\mathrm{.}5$ mark for lead time$)$ b$)$ Simulate CWD $\text{'}$s ordering and sales policy for $20$ weeks. $(12$ marks$)$ c$)$ Comnite tWe assume that no order is placed until the previous order arrives and the stock is used to

the reorder level.

The company has $3$ Printers in stock. Orders are always received at the beginning of the week. A

lead time of $2$ weeks imply that an order placed in week one will arrive in week $4.$

Required

a$)$ Construct the appropriate random number mappings for the random variables starting

with $\mathrm{.}00.(2\mathrm{.}5$ marks for demand and $1\mathrm{.}5$ mark for lead time$)$

b$)$ Simulate CWD $\text{'}$s ordering and sales policy for $20$ weeks. $(12$ marks$)$

c$)$ Compute the average cost of the policy $(4$ marks$)$

Use the following headingshe averaou cost of the nolicvi $4$ marks$)$ Use the following headings $($ PLEASE USE THE HEADINGS TO WHEN ANSWERING AS STATED