Consider a production cell with a single worker and several semiautonomous machines. Due to the

issues with the raw material used, with a two percent probability, a product may get stuck in a machine

after the processing, and a repair team is called to remove the product and recalibrate the machine if

that happens. The maintenance takes $45$ minutes to complete $($including the traveling time of the team$)$

and during the repair, the is a $40\%$ chance that the product gets damaged. The maintenance teams do

not end their shift before fixing a broken machine $($they work overtime if needed$).$ We know the following

parameters for the production system.

$$ There is a single shift in the factory that lasts $8$ hours. The workers take a $20-$minute break at the

middle of the shift.

$$ Machining time for a product is a random variable that is uniformly distributed between $5$ and $7$

minutes.

$$ The loading time is normally distributed with a mean of $45$ seconds and a standard deviation of $10$

seconds. Similarly, the unloading time is also normally distributed with a mean of $30$ seconds and a

standard deviation of $5$ seconds.

$$ The quality check takes $1$ minute for the worker $($if the part is not stuck$)$ and if a part is not stuck

the probability that it passes the quality check is $98\mathrm{.}5\%.$

$$ It takes $40$ seconds for a worker to move from one machine to the other one.

Use a simulation approach to answer the following questions.

$($a$)$ What would be the expected production quantities if $2,3,4$ or $5$ machines are placed in the production cell?

$($b$)$ Assume $3$ machines are placed in the cell. How much the daily production quantity would increase

if the stuck probability is reduced by $1$ percent?

$($c$)$ Assume $3$ machines are placed in the cell. How much the daily production quantity would increase if the successful production probability for the unstuck parts is increased by $1$ percent? Comment on the effectiveness of the system improvements in parts $($b$)$ and $($c$)$ by comparing the production

increases.