Problem #$6$: Supply Chain Disruption

Getting new products manufactured abroad and then delivered to their final destination in the

USA can be a challenging task. One US Company was tired of getting hit with product delays and

associated financial costs$/$penalties$.$ As a result, they culled through their individual records on $(1)$

their foreign manufacturer, $(2)$ their international delivery company, and $(3)$ their domestic

delivery company. All three had contributed to product delays at various times in the past.

After looking at historical data on actual cases, they discovered the following delays had been

observed $($relative to promised times$).$

After looking at historical data on actual cases, they discovered the following cost$/$financial penalty

had been observed $($$$/$day$).$ Obviously, longer delays are increasingly unfavorable, as reflected in

the following escalating $$-$penalty structure.

For example, a delay of $6$ days incurs a$$3,300$ penalty, while a delay of $36$ days incurs a $$30,600$

penalty.

For each simulated event, generate a unique random #$.$ And, assume $1$ Week $=1$ Calendar Week $(7$

days$),$ not $1$ Business Week $(5$ days$).$

$7$

a$)(5$ pts$)$ What is the expected $($i$.$e$.,$ average$)$ total delay, in days, for a new product?

b$)(5$ pts$)$ What is the probability that a new product$$s total delay is at least $1$ day?

c$)(5$ pts$)$ What is the probability that a new product$$s total delay is at least $5$ days?

d$)(5$ pts$)$ What is the probability that a new product$$s total delay is at least $15$ days?

e$)(5$ pts$)$ What is the expected $($i$.$e$.,$ average$)$ cost$/$financial penalty for product delays?