Using the graphical method to minimise the time required to process Job 1 and Job 2 on five machines A, B, C, D and E, find the minimum elapsed times an idle times to complete both jobs.
| Sequence | A | B | C | D | E | |
|---|---|---|---|---|---|---|
| Job 1 | Time (in hours) | 1 | 2 | 3 | 5 | 4 |
| Job 2 | Sequence | C | A | D | E | B |
| Time (in hours) | 3 | 4 | 2 | 1 | 5 |
We are asked to minimize the elapsed time and idle times for two jobs processed on five machines using the graphical (Gantt chart) method. Let’s solve it step by step manually. --- Step 1: Represent the jobs on the machines We have: | Machine | Job 1 Time | Job 2 Time | | ------- | ---------- | ---------- | | A | 1 | 3 | | B | 2 | 4 | | C | 3 | 2 | | D | 5 | 1 | | E | 4 | 5 | Job 2 sequence is given as C → A → D → E → B, which means Job 2 will visit C first, then A, then D, then E, then B. ________ _________ ____ ______ _____ __________ ____ ____ __________ _________ ____.
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A firm wants to know whether there is any linear relationship between the sales (X) and its yearly revenue (Y). The records for 10 years were examined and the following results were obtained:$
(a) Fit a regression line taking Y as the dependent variable and X as the independent variable.
(b) Test whether the sales have any effect on revenue at 5% level of significance.
(c) Comment on the goodness of fit of the regression line.
A company has three production facilities S1, S2 and S3 with production capacity of 7, 9 and 18 units (in 100s) per week of a product, respectively. These units are to be shipped to four warehouses D1, D2, D3 and D4 with requirement of 5, 6, 7 and 14 units (in 100s) per week, respectively. The transportation costs (in Rs) per unit between factories to warehouses are given in the table below:
| $D_1$ | $D_2$ | $D_3$ | $D_4$ | Capacity | |
|---|---|---|---|---|---|
| $S_1$ | 19 | 30 | 50 | 10 | 7 |
| $S_2$ | 70 | 30 | 40 | 60 | 9 |
| $S_3$ | 40 | 8 | 70 | 20 | 18 |
| Demand | 5 | 8 | 7 | 14 | 34 |
Using the graphical method to minimise the time required to process Job 1 and Job 2 on five machines A, B, C, D and E, find the minimum elapsed times an idle times to complete both jobs.
| Sequence | A | B | C | D | E | |
|---|---|---|---|---|---|---|
| Job 1 | Time (in hours) | 1 | 2 | 3 | 5 | 4 |
| Job 2 | Sequence | C | A | D | E | B |
| Time (in hours) | 3 | 4 | 2 | 1 | 5 |
Seven successive observations on a stationary time-series are as follows:
12, 14, 13, 10, 15, 12, 15
(a) Calculate auto-covariances C0, C1, C2, C3 and C4.
(b) Calculate auto-correlation coefficients r1, r2, r3 and r4.
(c) Plot the correlogram.
A researcher is interested in developing a linear model for the electricity consumption of a household having an AC (1.5 ton) so that she can predict the electricity consumption. For this purpose, she selects 25 houses and records the electricity consumption (in kWh), size of house (in square feet) and AC hours for one month during summers. The results obtained are:$
$
Build a regression model by selecting appropriate regressors in the model using the Stepwise Selection method.
Use the penalty (Big M) method to solve the following LP problem:
Minimise
Subject to the constraints.
Four professors are capable of teaching any one of four different courses. Class preparation time in hours for different topics varies from professor to professor and is given in the table below:
| Professor | A | B | C | D |
|---|---|---|---|---|
| Linear Programming | 2 | 15 | 13 | 4 |
| Queuing Theory | 10 | 4 | 14 | 15 |
| Transportation Problem | 9 | 14 | 16 | 13 |
| Regression Analysis | 7 | 8 | 11 | 9 |