Problem $1$ Consider a line with three stations in series. The processing times of stations $1,$

$2,$ and $3,$ are $30,30,$ and $31$ seconds, respectively. Each station has one worker. Assume that

the coefficient of variation $($CV$)$ of each station is $1$ and the arrival CV is also $1.$

$($a$)$ Calculate the total WIP if the line is run as a Push system with $TH=92$ jobs per hour

$($Round your final answer down to the nearest integer$).$ Note: I suggest you return to

original equations to solve this problem.

$($b$)$ Write the equation you used to calculate WIP in part $($a$).$

$($c$)$ If the system is run as a ConWIP line with WIP $=10,$ what is the line throughput?

$($d$)$ If the marginal profit per job is $$5$ and the cost for each unit of WIP $=$$$0\mathrm{.}50,$ use Solver

to calculate the maximum profit for both Push and ConWIP configurations of the line.

$($e$)$ Write the equation you used to calculate profit for the Push and ConWIP lines.