a$)$ Determine the value of $$ using Monte Carlo method. The diameter of the cirele is bunit $7+3=$

and the center is $(0,0).$ Do the simulation for $10$ pairs of random number and take half of $10$

a circle using second and third quadrant to do the simulation.a$)$ John arrives at a workstation at fixed intervals of one hour. Processing time is

approximately normal and has a mean of $56$ minutes per job and a standard deviation of

minutes per job. Simulate the system for $10$ jobs. Random values for processing: $0\mathrm{.}59,$

$-5\mathrm{.}67,0\mathrm{.}41,-2\mathrm{.}44,-3\mathrm{.}33,-0\mathrm{.}37,-4\mathrm{.}00,-0\mathrm{.}15,0\mathrm{.}99,-1\mathrm{.}60,-0\mathrm{.}88,0\mathrm{.}16,-2\mathrm{.}67,-3\mathrm{.}24,-4\mathrm{.}00.$

Determine operator idle time, job waiting time and percentage capacity utilization.