Time Limit: $45m.$

$11\mathrm{.}01\mathrm{.}24$

A restaurant finds that the average number of people waiting in line during lunch hour is $10.$ On average, during this period, $2$ people per minute leave the restaurant after receiving service. On average, how long do restaurant customers wait in line?

$I=$

$R=$

You are a purchasing manager in charge of stocking a certain type of transformer for a large electric utility. Weekly demand among your field crews for these transformers is normally distributed, with a mean of $100$ and a standard deviation of $50.$ Holding costs are $25$ percent, and you must hold a level of inventory corresponding to a cycle service level of $95$ percent. You are faced with two suppliers, Reliable Components and Value Electric, who offer the following terms. Reliable sells the transformer for $$5,000$ with a minimum order of $100,$ and a lead time of $1$ week with a standard deviation of $0\mathrm{.}1$ week. Value sells the transformer for $$4,800,$ has a minimum batch of $1,000,$ a lead time of $5$ weeks, and a lead$-$time standard deviation of $4$ weeks.

a$.$ What is the annual cost of using Reliable Components as a supplier? $($material cost $+$ handling cost of average inventory $+$ handling cost of safety stock$)$

b$.$ What is the annual cost of using Value Electric as a supplier?

c$.$ Which supplier would you choose?