State whether the following statements are True or False. Give reasons in support of your answers.
(a) The solution of a transportation problem with 5 rows (supplies) and 4 columns (destinations) is feasible if number of possible allocations are 8.
(b) The moving averages of suitable period in a time-series are free from the influences of seasonal and cyclic variations.
(c) If the basic solutions for a system of equations are (- 2, 0, 1), (0, 1, 3), (- 2, 3, 0), then only (0, 1, 3) is feasible.
(d) In the stepwise selection method of multiple regression model, once a variable enters in the model then it always remains in the model.
(e) An enterprise requires 1000 units per month. The ordering cost is estimated to be 50 per order. The purchase price is 20 per unit and the carrying cost per unit is 10% of it. Then the economic lot size to be ordered is 775.
________ _______ _________ __________ ________ _______ ___ _________ __________ _____.
_____ __________ ____ _________ _____ ___ _________ _________ ____ ________.
____ ________ ______ ____ ________.
________ ____ ______ _____ ___.
__________ ______ ______ _______ __________ ______ ____ ________.
_________ ________ _____ __________ ___ __________ _______ ______ ____ __________.
___ _______ ________ ____ ____ _________ ________ __________ _____.
_______ _______ ____ ______ ________.
____ ________ _______ _____ _____ _______ _______ ____ _______ _______ ____ _____.
___ ________ ___ ____ _________.
_____ _____ ______ _____ __________ ______ _______ _______ _______ _________ ___.
____ _____ _______ ________ ________ __________ _________ ______ _____ ___.
______ __________ ____ _____ ______ ________ ___ __________.
__________ _____ ____ __________ _______.
____ _____ _____ ___ ______ ________ ____ _________ ________.
______ ____ _________ _______ __________ _____ _______.
_______ ___ __________ _________ ____ _______ ____.
__________ __________ ____ ________ _________.
- Solved Assignments
- Study Notes
- Guess Papers
- Question Papers
✓ Unlock up to 60% of the answer
✓ No payment required
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 |
The following table represents the sales (in thousands) of mobile sets of a shop for 16 quarters over four years:
| Year | Quarter | |||
|---|---|---|---|---|
| Q_1 | Q_2 | Q_3 | Q_4 | |
| 2011 | 554 | 590 | 616 | 653 |
| 2012 | 472 | 501 | 521 | 552 |
| 2013 | 501 | 531 | 553 | 595 |
| 2014 | 403 | 448 | 460 | 480 |
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 |
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.
State whether the following statements are True or False. Give reasons in support of your answers.
(a) The solution of a transportation problem with 5 rows (supplies) and 4 columns (destinations) is feasible if number of possible allocations are 8.
(b) The moving averages of suitable period in a time-series are free from the influences of seasonal and cyclic variations.
(c) If the basic solutions for a system of equations are (- 2, 0, 1), (0, 1, 3), (- 2, 3, 0), then only (0, 1, 3) is feasible.
(d) In the stepwise selection method of multiple regression model, once a variable enters in the model then it always remains in the model.
(e) An enterprise requires 1000 units per month. The ordering cost is estimated to be 50 per order. The purchase price is 20 per unit and the carrying cost per unit is 10% of it. Then the economic lot size to be ordered is 775.
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 |
Use the penalty (Big M) method to solve the following LP problem:
Minimise
Subject to the constraints.