The following table represents the sales (in thousands) of mobile sets of a shop for 16 quarters over four years:
| Year | Quarter | |||
| Q1 | Q2 | Q3 | Q4 | |
| 2011 | 554 | 590 | 616 | 653 |
| 2012 | 472 | 501 | 521 | 552 |
| 2013 | 501 | 531 | 553 | 595 |
| 2014 | 403 | 448 | 460 | 480 |
(a) Compute the seasonal indices for four quarters by Simple average method. (b) Obtain deseasonlised values.
To compute the seasonal indices using the Simple Average Method and obtain the deseasonalized values, follow these steps: --- ### Step 1: Compute the Average Sales for Each Year We first calculate the average sales for each year. | Year | Q1 | Q2 | Q3 | Q4 | Yearly Average | |-------|-----|-----|-----|-----|---------------| | 2011 | 554 | 590 | 616 | 653 | \((554+590+616+653)/4 = 603.25\) | | 2012 | 472 | 501 | 521 | 552 | \((472+501+521+552)/4 = 511.5\) | | 2013 | 501 | 531 | 553 | 595 | \((501+531+553+595)/4 = 545\) | | 2014 | 403 | 448 | 460 | 480 | \((403+448+460+480)/4 = 447.75\) | --- ### Step 2: Compute ___ _______ _____ _______ _______ _____ __________ _____ _______ _______ _____ ____.
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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:
| Dl | D2 | D3 | D4 | Capacity | |
| S1 | 19 | 30 | 50 | 10 | 7 |
| S2 | 70 | 30 | 40 | 60 | 9 |
| S3 | 40 | 8 | 70 | 20 | 18 |
| Demand | 5 | 8 | 7 | 14 | 34 |
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.
Use the penalty (Big M) method to solve the following LP problem:
Minimise Z 5x1+ 3x2
Subject to the constraints:
The following table represents the sales (in thousands) of mobile sets of a shop for 16 quarters over four years:
| Year | Quarter | |||
| Q1 | Q2 | Q3 | Q4 | |
| 2011 | 554 | 590 | 616 | 653 |
| 2012 | 472 | 501 | 521 | 552 |
| 2013 | 501 | 531 | 553 | 595 |
| 2014 | 403 | 448 | 460 | 480 |
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.
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.
| Job 1 | Sequence | A | B | C | D | E | ||||
| Time (in hours) | 1 | 2 | 3 | 5 | 4 | |||||
| Job 2 | Sequence | C | A | D | E | B | ||||
| Time (in hours) | 3 | 4 | 2 | 1 | 5 | |||||
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.