PeloSpin $($PS$)$ makes quality bicycles to order, receiving customer orders online. Their most popular model is the Wave, which PS manufactures using the following process. First, John checks the order for consistency and prepares instructions for the subsequent operations. When the process operates at capacity, John$$s utilization is $40\%.$ Once John is done, the order moves to Amit and Lance, who can work on their respective tasks in parallel. Amit picks the correct frame from the inventory and spray paints the frame using PS$$s proprietary technology. When the flow balanced process operates at capacity, Amit$$s utilization is $100\%.$ When the frame is ready, Amit passes it on to final assembly and testing $($FAT$).$ Lance is in charge of wheel building and brake subassembly. Lance selects and mounts tires and disk brake rotors on the wheels to order based on the customer$$s weight. When the process operates at capacity, he is busy $60\%$ of the time. Once the wheels are ready, Lance passes them on to Beth whose tasks include assembling the shock absorbers and testing them together with the wheels on special equipment. Beth requires $20$ minutes for these tasks, and her utilization is $50\%$ when the process operates at capacity. When done Beth passes the tested wheels and shocks on to the FAT. At the final assembly and test, there are four equally competent workers: Britney, Tiffany, Avery, and Li$.$ When the frame, wheels, and shocks for a customer order are complete, one of these four workers assembles these components with other parts $($handlebar$,$ saddle, etc.$)$ into the finished bike. $($That is$,$ only one employee works on a given bike at FAT.$)$ When the process operates at capacity, the FAT resource pool$$s utilization is $80\%.$

a$)(5$ points$)$ Sketch the process flowchart

b$)(4)$ What is the theoretical capacity of the Wave production process in bikes per hour in steady state? $($There is no missing information!$)$

c$)(4)$ What are the activity times for all the activities of the Wave production process? $($in minutes$/$bike$)$

d$)(5)$ What is the theoretical flow time for a Wave bike? Can a bike arriving late in the day ever achieve it$?$

e$)(5)$ Lance and John have the following argument. Lance claims that it is possible to simultaneously increase the capacity and reduce the theoretical flow time of the Wave bike production process, simply by reducing the activity time of a single $($carefully selected$)$ activity while keeping the process otherwise unchanged. John, however, claims that this is not possible. Who is right and why?

f$)(6)$ Assume that Avery $($one of the people doing the final assembly and testing$)$ quits her job and no one replaces her. What impact does this have on the theoretical flow time and the theoretical capacity?