Question

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Information

Six months before its annual convention, the American Medical Association (AMA) must determine how many rooms to reserve. At this time, the AMA can reserve rooms at a cost of $100 per room. The AMA believes the number of doctors attending the convention will be has a triangular distribution with minimum value 2000, maximum value 7000, and most likely value 5000. If the number of people attending the convention exceeds the number of rooms reserved, extra rooms must be reserved at a cost of $ 160 per room. Assume that there are 8000 rooms available.

[Round your answers to the nearest integer. Also just enter the number. For example, if your answer is $123,456, then enter 123456 without $ and comma.]

Information

Build a simulation model assuming the number of doctors attending the convention follows the following probability distribution.

Number	Probability
2500	0.05
3000	0.07
3500	0.09
4000	0.1
4500	0.12
5000	0.2
5500	0.15
6000	0.1
6500	0.06
7000	0.04
7500	0.02

Run the simulation model 50,000 times.

Question 7 (3 points)

If they reserve 3000 rooms now, the expected total cost is

Your Answer:

Question 8 (3 points)

If they reserve 6000 rooms now, the expected total cost is

Your Answer:

Answer 1

We need to simulate the number of doctors attending the conference

the probability distribution of the number of doctors attending the conference, cumulative probability and the random number intervals for simulation are below

Number	Probability	Cumulative probability	Interval of random numbers
2500	0.05	0.05	0 to less than 0.05
3000	0.07	0.12	0.05 to less than 0.12
3500	0.09	0.21	0.12 to less than 0.21
4000	0.1	0.31	0.21 to less than 0.31
4500	0.12	0.43	0.31 to less than 0.43
5000	0.2	0.63	0.43 to less than 0.63
5500	0.15	0.78	0.63 to less than 0.78
6000	0.1	0.88	0.78 to less than 0.88
6500	0.06	0.94	0.88 to less than 0.94
7000	0.04	0.98	0.94 to less than 0.98
7500	0.02	1	0.98 to less than 1

To simulate the number of doctors attending the conference,  

• Draw a random number from standard uniform distribution using (=Rand())
• Compare the random number genearated agianst the interval of random number given the table above. The corresponding value in the column Number is the number of doctors attending the conference
• Do this 50000 times

Let X be the number of doctors who attend the conference and Y be the number of rooms reserved now (in advance)

the total cost = (Cost of reserving Y number of rooms) + (Extra Cost of reserving X-Y number of room if X>Y)

or

the total cost = (100*Y) + (if X>Y then [X-Y]*160, else 0 )

the following excel table shows the formula for calculating the total cost for 1 simulation

		Room Reserved
Random #	Number of doctors attending the conference	3000	6000
=RAND()	=IF(A3<0.05,2500,IF(A3<0.12,3000,IF(A3<0.21,3500,IF(A3<0.31,4000,IF(A3<0.43,4500,IF(A3<0.63,5000,IF(A3<0.78,5500,IF(A3<0.88,6000,IF(A3<0.94,6500,IF(A3<0.98,7000,7500))))))))))	=C$15*100+IF($B3>C$15,($B3-C$15)*160,0)	=D$15*100+IF($B3>D$15,($B3-D$15)*160,0)

One simulation with values looks like the following

This says that for simulation #1, the random number genearted is 0.377 and hence the number of doctors attending is 4500 and the total cost if 3000 room are reserved in advnace is $540,000 and if 6000 rooms are reserved in advance the total cost is $600,000

We need to replicate this 50,000 times. We do this by genearting 50,000 random numbers and copy the formulas in rest of the columns.

We get a sheet of the following nature, first few rows are displayed

Next we calculate the average total cost for 3000 rooms and 6000 rooms and that is the expected total cost

the expected costs are

Remember to paste the random numbers as values, as for every change new numbers are generated