Arrivals at telephone booth are considered to be Poisson with an average time of 10 minutes between are arrival and the next. The length of phone call is assumed to be distributed exponentially with mean 3 minutes.
i) What is the probability that a person arriving at the booth will have to wait?
ii) The telephone department will install a second booth when convinced that an arrival would expect waiting for at least 3 minutes for phone call. By how much should the flow of arrivals increases in order to justify a second booth?
iii) What is the average length of the queen that forms from time to time?
iv) What is the probability that it will take him or her more than 10 minutes altogether to wait for the phone and complete his or her call?
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For the following Auto regressive model
Xt = 0.7X t -1 - 0.4 Xt -2 + a t
i) Verify whether the series is Stationary
ii) Obtain pk : k = 1, 2 ,3, 4 and 5
iii) Plot the Correlogram.
The annual sales revenue (in lakhs of Rs) of a product as a function of sales force (number of salesmen) and annual adverting expenditure (in Thousands of Rs) for the past 10 years are summarised in following table:
| Annual Sales Revenue Y(in Lakhs) | Sales Force X1 (in Number) | Annual Advertising Expenditure X2 (in Thousand) |
| 100
115
125
135
105
145
110
120
135
175 | 40
65
40
90
115
80
50
60
70
100 | 140
115
190
80
100
140
115
150
130
160 |
A company makes two kinds of leather belts. Belt A is a high quality belt and Belt B is of lower quality. The respective profits are Rs 4 and Rs 3 per belt. The production of each of type A requires twice as much time as a belt of type B, and if all belts were of type B, the company could make 1000 per day. The supply of leather is sufficient for only 800 belts per day (Both A and B combined). Belt A requires a fancy buckle and only 400 per day are available. There are only 700 buckles a day available for Belt B. What should be the daily production of each type of belt? Formulate this problem as an LP Model and solve it using Simplex Method.
Find the sequence that minimizes the total elapsed time required to complete the following tasks on two machines:
|
Tasks: |
A |
B |
C |
D |
E |
F |
G |
H |
I |
|
Machine I: |
2 |
5 |
4 |
9 |
6 |
8 |
7 |
5 |
4 |
|
Machine II: |
6 |
8 |
7 |
4 |
3 |
9 |
3 |
8 |
11 |
State whether the following statements are true or false and also give the reason in support of your answer.
i) The number of possible basic solutions of an LPP of order 2 × 3 is 5.
ii) If there are 3 jobs to be performed one at a time on each of the 2 machines, then the possible number of sequences would be 36.
iii) If the arrival rate is 6 per hour and service rate is 3 per hour then the probability of no customer in queue is 0.7
iv) The estimated value of ‘b’ in the regression line Y = a + bX + e in terms of variancecovariance is
v) Given the trend equation, y = 108 + 2.88 with 1980 as origin and yearly data from 1980 to 1982, the estimated value for 1985 is 119.52.
A statistician collected data of 78 values with two independent variable X1 and X2 . The four models considered are:
(a) Y = B0 + e, (b) Y = B0 + B1X1 (c) Y = B0 + B1X1 + B2X2 + e and (d) Y = B0 + B2X2 + e. The results are SS(B0) = 6524. 2, SS(B0,B1) = 6793.4, SS(B0,B2) = 6540.0,SS(B0,B1,B2) = 6877.9 and Find additional contribution of (i) X2 overX1 and (ii) X1 overX2 . Test whether their inclusion in the model is justified.
A company has factories at F1 , F2 and F3 which supply to Ware houses at W1 , W2 and W3 .Weekly factory capacities are 200, 160 and 90 units, respectively. Weekly warehouse requirements are 180, 120 and 150 units, respectively. Unit shipping costs (in Rs) are as follows:
|
Factory | Warehouse |
Capacity | ||
| w1 | w 2 | w 3 | ||
| F1 | 16 | 20 | 12 | 200 |
| F2 | 14 | 8 | 18 | 160 |
| F3 | 26 | 24 | 16 | 90 |
| Demand | 180 | 120 | 150 | 450 |