# IGNOU MSTE-002 Solved Assignment 2022

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## IGNOU MSTE-002 Solved Assignment 2022

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 Assignment Paper IGNOU MSTE-002 Solved Assignment 2022 Subject Name Industrial Statistics-II No.of Pages in Solution 38 Course PGDAST Language ENGLISH Session 2022 Last Date for Submission of Assignment For June Examination 31st March 2022 or as per dates given in the Ignou website For December Examination 30th September 2022 or as per dates given in the Ignou website

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## IGNOU MSTE-002 Sample Solution 2022

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## IGNOU MSTE-002 Solved Assignment 2022

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## (Industrial Statistics-II)

MSTE-002: Industrial Statistics-II

1.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.

2. Use the penalty (Big M) method to solve the following LP problem:

Minimise Z = 5x1+ 3x2

Subject to the constraints 2x1+ 4x2 ≤ 12
2x1+ 2x2 = 10
5x1+ 2x2 ≥ 10

xl, x2 ≥ 0.

3. 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:

 D1 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

Obtain optimal solution by the MODI method.

4. 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

Each professor is assigned only one course. Determine an assignment schedule so as to minimise the total course preparation time for all

courses.

5. In a railway marshalling yard, goods trains arrive at a rate of 36 trains per day. Assuming that the inter-arrival and service time

distributions both follow exponential distribution with an average of 30 minutes, calculate the following:

(i)  Traffic intensity

(ii)  The mean queue length

(iii) Probability that the queue size exceeds

6. 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

7. 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:

$\sum _{n=1}^{10}\:X=265,\sum \:_{n=1}^{10}\:Y=27.73,SS_x=285.6,SS_y=6.978,SS_{xy}=57.456$

(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.

8. 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:

​​

\begin{array}{l}
\hat{\mathrm{B}}_{0}=22.38, \hat{\mathrm{B}}_{1}=1.6161, \hat{\mathrm{B}}_{2}=0.0144, \operatorname{SS}\left(\mathrm{B}_{0}\right)=12526.08, \mathrm{SS}\left(\mathrm{B}_{0}, \mathrm{~B}_{1}\right)=17908.47, \mathrm{SS}\left(\mathrm{B}_{0}, \mathrm{~B}_{2}\right)= \\
17125.23, \mathrm{SS}\left(\mathrm{B}_{0}, \mathrm{~B}_{1}, \mathrm{~B}_{2}\right)=18079.0, \hat{\sigma}^{2}=10.53, \mathrm{SE}\left(\hat{\mathrm{B}}_{1}\right)=0.17, \text { and } \mathrm{SE}\left(\hat{\mathrm{B}}_{2}\right)=0.0035 .
\end{array}

Build a regression model by selecting appropriate regressors in the model using the Stepwise Selection method.

9. 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.

Insert math as
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