Problem $7(20$ pts$)$

Consider a manufacturing network of three queues: A$,$ B$,$ and C$.$ Items arrive at queue A at a

rate of $12$ per hour. Once served at A$,$ they move to queue B$,$ where the service rate is $10$

customers per hour. After queue $B,$ they move to queue $C$ with a service rate of $8$ customers

per hour. Each machine $($A$,$ B& C$)$ has a different running cost.

A B C

Labor Hours per

unit

$2\mathrm{.}2,0\mathrm{.}4,1\mathrm{.}1$

Labor Cost per

$Hr$

$$30$$$42$$$20$

Machine Costs

$($depreciation$,$

power,

$$66$$$22$$$320$

maintenance,

etc$)$ per hour

Calculate

the average number of items in each queue

the average time an item spends in the entire system.

The cost to balance the system so there are no queues. This answer is unlikely to be an

integer value$($your formula will suggest adding$/$subtraction a partial machine or person$)$