Prblm 1: Students arrive at the Administrative Services Office at an average of one every 15 minutes and their requests take on average 10 minutes to be
processed. The service counter is staffed by only one clerk Judy Gumshoes who works eight hours per day. Assume Poisson arrivals and exponential service
times.

a) what percentage of time is Judy idle?

b)How much time on average does a student spend waiting in line?

c)how long is the (waiting) line on average?

What is the probability that an arriviing student ( just before entering the administrative services office) will find at least one other student waiting in
line?

question 2

Burrito King ( a new fast-food franchise opening up nationwide) has successfully automated burrito production for its drive-up fast-food establishments. The
Burro-Master 9000 requires a constant 45 seconds to produce a batch of burritos. It has been estimated that customers will arrive at the drive up window
according to a poisson distribution at an average of one every 50 seconds. To hlp determine the amount of space needed for the line at the drive up window.
Burrito king would like to know the expected average time in the system the average line length (in cars) and the average number of cars in the system (both
in line and at the window).

question 3

DAT Inc. needs to develop an aggregate plan for its product line. Relevant data are as follows:

Production time 1 hour per unit Beginning inventory 500 units

Average labor cost $10 per hour Safety stock One-half month

workweek 5 days 8 hours each day Shortage cost $20/unit/month

The forecast for next year is

Jan 2500 Feb 3000 Mar 4000 Apr 3500 may 3500 june 3500 july 3000 aug 4000 sept 4000 oct 4000 nov 3000 dec 3000

Management prefers to keep a constant workforce and production level absorbing variations in demand through inventory excesses and shortages. Demand not met
is carried over to the following month.

Develop an aggregate plan that will meet the demand and other conditions of the problem. Do not try to find the optimum; just find a good solution and state
the procedure you might use to test for a better solution. Make any necessary assumptions.

question 4

Audio products Inc. produces 2 AM/FM/CD players for cars. The radio/CD units are identical but the mounting hardware and finish trim differ. The standard
model fits intermediate and full size cars and the sports model fits small sports cars.

Audio Products handles the production in the following way. The chassis (radio/CD unit) is assembled in Mexico and has a manufacturing lead time of two weeks.
The mounting hardware is purchased from a sheet steel company and has a 3 week lead time. The finish trim is purchased from a Taiwan electronics company with
offices in ALos Angeles as prepackeaged units consisting of knobs and various trim pieces. Trim packages have a 2 week lead time. Final assembly time may be
ddisregarded because adding the trim package and mounting are performed by the customer.

Audio products supplies wholesalers and retailers who place specific orders for both models up to eight weeks in advance. These order together with enough
additional units to satisfy the small nmber of individual sales are summarized in the following demand schedule:

WEEK

Model 1 2 3 4 5 6 7 8

Standard model for week 4 was 300 and week 8 was 400

sports model for week 5 was 200 and week 8 was 100

There are currently 50 radio/CDE units on hand but no trim packages or mounting hardware.

Prepare a material requirements plan to meet the demand schedule exactly. Specify the gross and net requirements on hand amounts and the planned order
release and receipt periods for the radio/CD chassis the standard trim and sports car model trim and the standard mounting hardware and the sports car
mounting hardware.