CLASS PROJECT
THE CLASS PROJECT BELOW INCLUDES TWO CASES. FOR FULL CREDIT, WRITEUPS FOR BOTH CASES MUST BE COMPLETED!!!!!! FOR EACH CASE, INCLUDE A BRIEF SUMMARY OF THE CASE, A MODEL FORMULATION, ANY COMPUTATIONS AS APPROPRIATE, AND AN ANALYSIS OF RESULTS. INCLUDE ANY RECOMMENDATIONS AND CONCLUSIONS YOU FEEL ARE APPROPRIATE. REMEMBER TO COMPLETE BOTH CASES!!!!!
NOTE THAT THE PROJECT IS GRADED OUT OF 20 POINTS - 10 POINTS FOR EACH CASE!!!!
10 PTS. I) THE TEN STARS AMUSEMENT PARK
THE TEN STARS TRAVELING AMUSEMENT PARK HAS RECENTLY SET UP OPERATION IN THE EAST BAY. THE ARRIVAL RATE OF PATRONS AT THE PARK IS ESTIMATED AS 30 PER HOUR. THERE IS ONE ADMISSIONS GATE, STAFFED BY A SINGLE WORKER. ADMISSIONS CAN BE CONDUCTED AT AN ESTIMATED RATE OF 35 PER HOUR. FORTY PERCENT OF PATRONS GO DIRECTLY TO THE FERRIS WHEEL, WHILE THE OTHER SIXTY PERCENT
GO TO THE ROLLERCOASTER. THE SERVICE RATE OF THE FERRIS WHEEL IS 15 PATRONS PER HOUR, WHILE THE SERVICE RATE OF THE ROLLER COASTER IS 24 PATRONS PER HOUR. ALL OF THE PATRONS LEAVING THE FERRIS WHEEL GO TO THE HOUSE OF MIRRORS. IN ADDITION, THIRTY PERCENT OF PATRONS LEAVING THE ROLLER COASTER GO TO THE HOUSE OF MIRRORS. THE HOUSE OF MIRRORS SERVES PATRONS ONE AT A TIME AT A RATE OF 20 PER HOUR. ALL PATRONS LEAVING THE HOUSE OF MIRRORS AS WELL AS REMAINING PATRONS LEAVING THE ROLLERCOASTER ALL GO TO THE EXIT GATE. THERE IS ONE WORKER AT THE EXIT GATE, WHO CAN PROCESS EXITING PATRONS AT A RATE OF 37 PER HOUR.
IT IS DESIRED TO DETERMINE FOR THIS AMUSEMENT PARK, THE EXPECTED NUMBER OF PATRONS WAITING AT THE ADMISSION GATE, EXIT GATE, AND AT EACH RIDE. IT IS ALSO DESIRED TO DETERMINE THE EXPECTED TIME PATRONS SPEND WAITING AT EACH OF THESE LOCATIONS. IF AN ADDITIONAL WORKER WAS AVAILABLE, AT WHICH "STATION" (I.E., ENTRY GATE, EXIT GATE,
OR RIDE) SHOULD THIS WORKER BE PLACED?
THE DEPT. OF PUBLIC SAFETY FOR ALAMEDA COUNTY WOULD LIKE TO KNOW WHAT THE AVERAGE NUMBER OF PATRONS IS EXPECTED TO BE IN THE PARK OVER THE COURSE OF A DAY IN ORDER TO DETERMINE WHETHER THIS MEETS WITH SAFETY REGULATIONS. CURRENT REGULATIONS DO NOT ALLOW FOR MORE THAN 25 PATRONS IN THE PARK AT ANY ONE TIME. WHAT WOULD YOU REPORT FOR THIS? (I.E., IS THE REQUIREMENT MET?) (NOTE THAT YOU CAN TREAT EACH STATION AS
A SINGLE SERVER SYSTEM!!!!!) MAKE SURE TO SHOW YOUR CALCULATIONS AND REPORT YOUR RESULTS REGARDING PARK OPERATIONS.
A) WRITE A SHORT SUMMARY OF THE CASE, INCLUDING THE PURPOSE OF YOUR ANALYSIS.
B) SHOW AND EXPLAIN THE MODEL YOU USED TO EVALUATE THE AMUSEMENT PARK SYSTEM.
C) SHOW ANY CALCULATIONS YOU USED TO OBTAIN YOUR RESULTS. (HINT: FOR EACH GATE AND RIDE YOU WILL NEED L, Lq, and Wq.)
D) DISPLAY A SUMMARY OF RESULTS.
E) ANSWER ANY QUESTIONS POSED WITH THE CASE IN ADDITION TO THE SUMMARY OF RESULTS. (I.E., AT WHAT RIDE WOULD YOU PLACE AN ADDITIONAL WORKER, AND ARE PARK LIMITATIONS ON PATRONS BEING MET?)
F) WRITE A BRIEF CONCLUSIONS AND RECOMMENDATIONS. A FEW SENTENCES WILL SUFFICE.
10 PTS. II) THE MAIN STREET DELI - ROTISSERIE CHICKEN THE MAIN STREET DELI IN HAYWARD PREPARES ROTISSERIE CHICKEN FOR PATRONS WHO COME IN AT THE END OF THE DAY AFTER WORK.
CURRENTLY, THE DAILY DEMAND FOR THESE ROTISSERIE CHICKENS AT THE END OF THE DAY HAS BEEN FOUND TO BE DISTRIBUTED AS FOLLOWS (BASED ON HISTORICAL DATA):
#ROTISSERIE PERCENT
CHICKENS OF DAYS
0 .10
1 .30
2 .30
3 .15
4 .15
THE DELI IS NOT CONSISTENT WITH REGARD TO HOW MANY OF THESE CHICKENS THEY CAN BAKE DAILY. THIS IS BECAUSE THEY HIRE A NUMBER OF C.S.U.E.B. STUDENTS TO WORK DAILY, AND SOME ARE NOT AVAILABLE BECAUSE OF SCHOOL COMMITMENTS.
BASED ON PAST DATA, THE NUMBER OF CHICKENS WHICH CAN BE BAKED ON A GIVEN DAY IS DISTRIBUTED AS FOLLOWS. NOTE THAT IF ON ANY DAY AN EXCESS OF CHICKENS ARE BAKED, THEY WILL BE DISPOSED OF AND CANNOT BE SAVED FOR LATER USE. ALSO, IF THERE IS AN EXCESS OF DEMAND ON ANY GIVEN DAY, THIS DEMAND WILL BE LOST.
# CHICKENS
BAKED PERCENT OF DAYS
2 .50
3 .30
4 .10
5 .10
THE ROTISSERIE CHICKENS ARE SOLD FOR $10 EACH, AND COST $3 TO BAKE. CONDUCT A SIMULATION OF CHICKENS BAKED AND SOLD DAILY FOR 30 DAYS. YOU CAN USE THE RANDOM NUMBER TABLES IN THE CLASS HANDOUT ON SIMULATION, OR ANY OTHER SOURCE OF RANDOM NUMBERS YOU CHOOSE!!!!!! (NOTE THAT YOU WILL NEED SEPARATE RANDOM NUMBERS TO GENERATE THE NUMBER OF CHICKENS BAKED DAILY, AND THE DAILY DEMAND FOR CHICKENS!!)
A) DEFINE YOUR RANDOM NUMBER RANGE TABLES.
B) SHOW YOUR SIMULATION TABLE. INCLUDE COLUMNS FOR
- THE NUMBER OF CHICKENS BAKED DAILY
- THE DAILY DEMAND FOR BAKED CHICKENS
- THE NUMBER OF CHICKENS SOLD DAILY
- EXCESS CHICKENS BAKED DAILY (NOT SOLD)
- SHORTAGE OF CHICKENS DAILY (UNMET DEMAND)
C) BASED ON YOUR SIMULATED RESULTS, WHAT IS THE AVERAGE DAILY PROFIT MADE? SHOW YOUR CALCULATION.
B) HOW MUCH DEMAND FOR CHICKENS IS LOST, AGAIN ON AN AVERAGE DAILY BASIS?
C) HOW MANY CHICKENS ARE DISPOSED OF, AGAIN ON AN AVERAGE DAILY BASIS?
D) DO YOU BELIEVE YOU ARE BAKING TOO MANY CHICKENS RELATIVE TO DEMAND? EXPLAIN YOUR REASONING.
MAKE SURE TO SHOW YOUR SIMULATION TABLE AND THE RANDOM NUMBERS YOU ASSIGNED.