IGNOU PGDAST MSTE 002 Industrial Statistics-II Solved Assignment ENGLISH

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MSTE 002 (January 2026 - July 2026) - ENGLISH

TUTOR MARKED ASSIGNMENT

MSTE-002: Industrial Statistics-II

Course Code: MSTE-002
Assignment Code: MSTE-002/TMA/2026
Maximum Marks: 100

Note: All questions are compulsory. Answer in your own words.

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.

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

Minimise

Subject to the constraints







.

2. 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

Obtain optimal solution by the MODI method

3. 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.

4. 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

5. 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

6. 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.

7. 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. 

8. 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) Compute the seasonal indices for four quarters by Simple average method.
(b) Obtain deseasonlised values.
9. 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.

 

 

 

 

 

MSTE 2 2025 - English

MSTE-002: Industrial Statistics-II

Course Code: MSTE-002

Assignment Code: MSTE-002/ΓΜΑ/2025

Maximum Marks: 100

Note: All questions are compulsory. Answer in your own words.

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:

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:

	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

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:

(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:

SS(B₀) = 12526.08, SS(B₀,B₁) = 17908.47, SS(B₀,B₂) = 17125.23, SS(B₀, B₁, B₂) = 18079.0,

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.

10. 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.

 

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