Extra Question for $10$ bonus points.

The preinduction physical examination given by the US Army involves the following seven activities. These activities can be performed in any order, with two exceptions: the medical history must be taken first and the exit medical evaluation is the final step. At present there are three paramedics and two physicians on duty during each shift. The maximum number of people can work together in one workstation is two. Only a physician can perform the exit evaluation or conduct the psychological interview. Other activities can be carried out by either physicians or paramedics. Also suppose that the maximum number of people can work together in one workstation is two. $(10$pt$)$

$\backslash$table$[[$Activity$,$Average time $($minutes$)],[$Medical history,$13],[$Blood tests,$6],[$Eye examination,$7],[$Measurements $($weight$,$ height, etc.$),9],[$Medical examination,$16],[$Psychological interview,$12],[$Exit medical evaluation,$10]]$

a$.$ Draw the flowchart to develop an examination process layout to balance the line. Hint: group activities into different workstations to achieve the maximum process capacity.

b$.$ What is the cycle time of this examination process?

c$.$ Which workstation is the bottleneck in the examination process layout?

d$.$ How many people can be processed per hour $($throughput rate of the examination process$)?$