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 |
How should the Job be allocated, one per employee, so as to minimise the total man-hours?
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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 production department for a company requires 3600 kg of raw material for manufacturing a particular item per year. It has been estimated that the cost of placing an order is Rs 36 and the cost of carrying inventory is 25 percent of the investment in the inventories. The price is Rs10 per kg. The purchase manager wishes to determine an ordering policy for raw material.
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.
The demand (in thousands of units) of refrigerators manufactured by a company are summarised in the following table:
| Year | Quarter | |||
| I | II | III | IV | |
| 2011 2012 2013 2014 | 124 104 80 116 | 120 128 152 156 | 176 148 168 184 | 140 132 156 180 |
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.