# task problem set 8 due 3-30-14

## Project Description:

task problem set 8

due date: mar 30, 2014 23:59:59 max points: 130

details: complete problems b.1, b.5, b.7, d.1, and d.9 (parts a through e; assume µ = 15).
for problems requiring computations, please ensure that the excel file includes the associated cell computations; this information is needed in order to receive full credit on these problems.
note that for problems that require diagrams, it is suggested that the student use microsoft visio. microsoft powerpoint or the drawing tools provided by microsoft excel may also be used.
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b.7 the attaran corporation manufactures two electrical
products: portable air conditioners and portable heaters. the
assembly process for each is similar in that both require a certain
amount of wiring and drilling. each air conditioner takes 3 hours
of wiring and 2 hours of drilling. each heater must go through
2 hours of wiring and 1 hour of drilling. during the next production
period, 240 hours of wiring time are available and up to
140 hours of drilling time may be used. each air conditioner sold
yields a profit of \$25. each heater assembled may be sold for a
\$15 profit.
formulate and solve this lp production-mix situation, and
find the best combination of air conditioners and heaters that
yields the highest profit.
d.1 customers arrive at rich dunn’s styling shop at a
rate of 3 per hour, distributed in a poisson fashion. rich can perform
haircuts at a rate of 5 per hour, distributed exponentially.
a) find the average number of customers waiting for haircuts.
b) find the average number of customers in the shop.
c) find the average time a customer waits until it is his or her
turn.
d) find the average time a customer spends in the shop.
e) find the percentage of time that rich is busy.
d.9 (parts a through e; assume µ = 15).
d.9 neve commercial bank is the only bank in the town
of york, pennsylvania. on a typical friday, an average of 10 customers
per hour arrive at the bank to transact business. there is
currently one teller at the bank, and the average time required to
transact business is 4 minutes. it is assumed that service times may
be described by the exponential distribution. if a single teller is
used, find:
a) the average time in the line.
b) the average number in the line.
c) the average time in the system.
d) the average number in the system.
e) the probability that the bank is empty.
f) ceo benjamin neve is considering adding a second teller
(who would work at the same rate as the first) to reduce the
waiting time for customers. a single line would be used, and
the customer at the front of the line would go to the first available
bank teller. he assumes that this will cut the waiting time
in half. if a second teller is added, find the new answers to
parts (a) to (e).
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