A CONWIP flow line system has three stations in series. The first station has a processing

time of $3$ minutes, the second one a processing time of $3$ minutes, and the third a processing

time of $1$ minute. The flow system has constant WIP since it is closed.

a$.(5)$ Construct a Gantt chart for the flow system when w$=2$ so that steady state is achieved.

b$.(5)$ Construct a Gantt chart for the flow system when w$=3$ so that steady state is achieved.

c$.(5)$ What is the raw processing time, the bottleneck rate and the critical WIP of the line?

d$.(5)$ What is the steady$-$state utilization of the bottleneck station for both cases?

e$.(5)$ Graph CT and TH as continuous functions of w using the equations from class and

verify the values from your Gantt chart analysis using w$=2$ and w$=3.$