Demand for widgets follow the probability distribution shown:

Stock is examined every $7$ days $($the plant is in operation every

day$)$ and if the stock level has reached $6$ units, or less, an order

for $10$ widgets is placed. The lead time $($days until delivery$)$ is

probabilistic and follows the following distribution:

When the simulation begins, it is the beginning of the week, $12$

widgets are on hand, and no backorders are allowed. Stock is

delivered at the start of the day, ready for sale for that

day. Simulate for $6$ weeks of operation of this system. Analyze

the system. Perform additional simulations to determine

the effect on shortages if increases or decreases occur in:

$(1)$ the review period $($if instead of $7$ days it was $5$ days, or $11$

days$),$

$(2)$ the reorder quantity Q $($if instead of $10$ units it was higher

$[15]$ or lower $[6]),$ and

$(3)$ the reorder point $R($if instead of $6$ units it was higher $[11]$ or

lower $[3]).$