Question

A specialist electronics company carries out its own repairs. The manager of the repair center is becoming concerned that the cost of repairs is continually increasing. She has observed the operations of the repair center and collected data relating to the number of items being repaired each day, and also the cost of repairing these items over a 50-day period. This information is presented in the following tables:

Repairs per day	Probability
1	0.08
2	0.22
3	0.38
4	0.26
5	0.06

Cost of repair ($)	Probability
5	0.28
10	0.42
15	0.22
20	0.06
25	0.02

Use the following series of random numbers to simulate the number and total daily cost of repairs carried out by the department over a 5-day period. Use the following random numbers in order (from left to right) for the simulation of repairs per day:

0.05

0.33

0.25

0.57

0.90

Use the following random numbers in order (from left to right, first row first - as you need them) for the simulation of the cost of repairs:

0.01	0.46	0.21	0.78	0.99	0.06	0.20	0.96	0.81	0.18
0.03	0.67	0.26	0.19	0.90	0.32	0.86	0.10	0.84	0.76

Please note you may find that you do not need all of the last sequence of 24 random numbers.


What is the total cost of repairs after 5 days of simulation?

Answer 1

Solution

Preparatory Work

Random Number Assignment
Repairs per day	Probability		Cumulative Probability			Random numbers assigned
1	0.08		0.08			0.01 - 0.08
2	0.22		0.3			0.09 - 0.30
3	0.38		0.68			0.31 - 0.68
4	0.26		0.94			0.69 - 0.94
5	0.06		1			0.95 - 0.00
Cost of repair ($)		Probability		Cumulative Probability			Random numbers assigned
5		0.28		0.28			0.01 - 0.28
10		0.42		0.7			0.29 - 0.70
15		0.22		0.92			0.71 - 0.92
20		0.06		0.98			0.93 - 0.98
25		0.02		1			0.99, 0.00

Back-up Theory

Total Cost of Repair per Day = (Number of Repairs per Day) x (Repair Cost per Repair)

Now to work out the solution,

Following codes are employed for ease in presentation.

RN: Random Number; NR: Number of Repairs per Day; CR: Repair Cost per Repair

TC: Total Cost of Repair per Day

Five-day Simulation

Day	Repairs per Day		Cost per Repair		TC
	RN	NR	RN	CR
1	0.05	1	0.01	5	5
2	0.33	3	0.46	10	30
3	0.25	2	0.21	5	10
4	0.57	3	0.78	15	45
5	0.90	4	0.99	25	100
				Total	190

Thus, total cost of repair for the 5-day period = $190 ANSWER

DONE