What will be the average number of scooters waiting in the factory?

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written 8.4 years ago by

teamques10 ★ 68k

• modified 4.0 years ago

The automobile company manufactures around 150 scooters. The daily production varies from 146 to 154 depending upon the availability of raw materials and other working conditions: -

Production per day	Probability
146	0.04
147	0.09
148	0.12
149	0.14
150	0.11
151	0.10
152	0.20
153	0.12
154	0.08

The finished scooters are transported in a specially arranged lorry accommodating 150 scooters. Using the random numbers 80, 81, 76, 75, 64, 43, 18, 26, 10, 12, 65, 68, 69, 61, 57, simulate the process to find out: - i. What will be the average number of scooters waiting in the factory? - ii. What will be the average number of empty space on the lorry? -

operation research

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1 Answer

1.1kviews

written 8.4 years ago by

teamques10 ★ 68k

modified 2.7 years ago by

jitendrakumargothi2735 • 30

Production per day	Probability	Cumulative Probability	Random Numbers Assigned
146	0.04	0.04	00-03
147	0.09	0.13	04-12
148	0.12	0.25	13-24
149	0.14	0.39	25-38
150	0.11	0.50	39-49
151	0.10	0.60	50-59
152	0.20	0.80	60-79
153	0.12	0.92	80-91
154	0.08	1.00	92-99

Using the given random numbers, the process is simulated:

Lorry capacity = 150

Day	Random Number	Production	Can be transported in Lorry	Scooters waiting at factory	Cumulative no. of Scooters waiting at factory	Scooters actually transported by Lorry
1	80	153	150	3	3	150
2	81	153	150	3	6	150
3	76	152	150	2	8	150
4	75	152	150	2	10	150
5	54	151	150	1	11	150
6	43	150`	150	0	11	150
7	18	148	148	-	9	150
8	26	149	149	-	8	150
9	10	147	147	-	5	150
10	12	147	147	-	2	150
11	65	152	150	2	4	150
12	68	152	150	2	6	150
13	69	152	150	2	8	150
14	61	152	150	2	10	150
15	57	151	150	1	11	150

1.Average number of scooters waiting at the factory:

Total number of scooters waiting at the factory over the 15 day period: 3+3+2+2+1+2+2+2+2+1 = 20

Therefore average number waiting = 20 / 15 = 1.33 / day

Or 20 / 15 day period

2.Average number of empty spaces in the lorry:

As evident from the table above, in any 15-day period, the lorry always goes full.

Hence there is no empty space in the lorry.

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