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 |
Obtain a regression model to forecast the annual sales revenue of the product using Matrix Method.
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A private company has two bottling plants located in city I and City II. Each plant produces three cold drinks Drink A, Drink B and Drink C. The number of bottles produced per day are as follows.
| Drink | Plant at | |
| City I | City II | |
| Drink A | 1,500 | 1,500 |
| Drink B | 3,000 | 1,000 |
| Drink C | 2,000 | 5,000 |
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.
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 |
A department has five employees with five jobs to be performed. The time (in hours) each man will take to perform each job is given in the effectiveness matrix:
| Employees | |||||
| Jobs | I | II | III | IV | V |
| A B C D E | 10 3 10 7 7 | 5 9 7 11 9 | 13 18 2 9 10 | 15 13 2 7 4 | 16 6 2 12 12 |
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 |