A production flow line consisting of four workstations in series produces circuit boards. The first workstation consists of a screen-printing operation that takes 30 seconds per board. The second workstation has three placement machines running in parallel (i.e., a board only goes to one of them) that put components on boards, using 1 minute and 45 seconds per board. The third workstation consists of a reflow oven that requires 38 seconds per board. The final workstation consists of two parallel inspection devices that takes 66 seconds per board.

Cycle time (CT) is the average time it takes a board to progress through the entire line, work in process (WIP) is the number of boards between the beginning and end of the line, and throughput (TH) is defined as the average number of boards produced per minute. Your job is to do the following: for WIP levels between 1 and 15, compute CT and TH and plot these relationships. If "critical WIP" is defined as the smallest WIP level that achieves the maximum throughput, compute this value as well. Finally, describe formally, the relationship (if any) between WIP, CT and TH?