# MSTE-002 Solved Assignment 2021

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## MSTE-002 Solved Assignment 2021

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## MSTE-002 Solved Assignment 2021

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## (Statistical Techniques)

MSTE-002: Industrial Statistics-II

1. State whether the following statements are true or false and also give the reason in support of your answer.
1. If the arrival rate is 12 per hour and service rate is 4 per hour, then the probability of no customer in queue is 0.3.
2. If the coefficient of determination is 0.833, the number of observations and independent variables are 12 and 3, respectively, then Adjusted R2 will be 0.84.
3. The Set S ={(x, y) : 0 ≤ y ≤ 5 when 0 ≤ x ≤ 2 and 3 ≤ y ≤ 5 when 2 ≤ x ≤ 7 } is not a convex set.
4. The solution to a transportation problem with 3-rows (supplies) and 3-columns (destinations) is feasible if number of positive allocations is 6.
5. Variations which occur due to natural forces and operate in a regular and periodic manner over a span of less than or equal to one year are termed as cyclic variations.
2. Solve the following LPP using simplex method:

Maximize Z = 10 x1 + x2 + 2x3           Subject to the constraints:

4x1 + x2 – 6x3 = 7

6x1+ x2 – 4x3 ≤ 5

3 x1 – x2 – x3 ≤ 0

x1, x2, x3 ≥ 0

1. Let X is the advertisement expenditures (in Lakh Rs.) and Y is the sales (in Lakh Rs.). Let the data are
 X: 1182 1172 1264 1493 1571 1711 1804 1840 1956 1954 Y: 129 135 147 160 171 184 198 223 240 293

Estimate the parameters and find the estimated linear equation. Whether the advertisement

influences the sale of product? Test and comment on the goodness of fit of the model.

1. a) The production department for a company requires 3600 kg of raw material for manufacturing a particular item per year. It has been estimated that the cost of placing an order is Rs 36 and the cost of carrying inventory is 25 percent of the investment in the inventories. The price is Rs10 per kg. The purchase manager wishes to determine an ordering policy for raw material.
2. b) Arrivals at telephone booth are considered to be Poisson with an average time of 10 minutes between are arrival and the next. The length of phone call is assumed to be distributed exponentially with mean 3 minutes.
1. What is the probability that a person arriving at the booth will have to wait?
2. The telephone department will install a second booth when convinced that an arrival would expect waiting for at least 3 minutes for phone call. By how much should the flow of arrivals increases in order to justify a second booth?
• What is the average length of the queen that forms from time to time?
1. What is the probability that it will take him or her more than 10 minutes altogether to wait for the phone and complete his or her call?

1. The annual sales revenue (in lakhs of Rs) of a product as a function of sales force (number of salesmen) and annual adverting expenditure (in Thousands of Rs) for the past 10 years are summarised in following table:
 Annual Sales Revenue Y(in Lakhs) Sales Force X1 (in Number) Annual Advertising Expenditure X2 (in Thousand) 100 115 125 135 105 145 110 120 135 175 40 65 40 90 115 80 50 60 70 100 140 115 190 80 100 140 115 150 130 160

Obtain a regression model to forecast the annual sales revenue of the product using Matrix

Method.

1. A solicitors’ firm employs typists on hourly price-rate basis for their daily work. There are five typists and their charges and speed are different. According to an earlier understanding only one job is given to one typist and the typist is paid for a full hour even if he works for a fraction of an hour. Find the least cost allocation for the following data:
 Typist Jobs P Q R S T A B C D E 85 90 75 80 76 75 78 66 72 64 65 66 57 60 56 125 132 114 120 112 75 78 69 72 68

1. a) Obtain seasonal Indices by the “Moving average” method from the following data:
 Quarterly output of a Factory Year I II III IV 2010 2011 2012 2013 65 68 70 60 58 63 59 55 56 63 56 51 61 67 52 58

(b)         For the following Auto regressive model

Xt = 0.7Xt1 −0.4Xt2 +at

1. i) Verify whether the series is Stationary
2. ii) Obtain ρk : k =1,2,3,4 and 5

Plot the Correlogram.

1. a) A company has three production factories S1, S2 and S3 with production capacity of 7, 9 and 18 units (in 100 s) per week of a product, respectively. These units are to be shipped to four warehouses D1, D2, D3 and D4 with requirements of 5, 8, 7 and 14 units (in 100’s) per week, respectively. The transportation costs (in rupees) per unit between factories to ware houses are given in table below.

Obtain the initial basic solution using LC Method and also obtain the optimum solution

using MODI method.

1. b) Twenty-five successive observations on a stationary time series are given as follows:

30, 33, 32, 27, 25, 28, 29, 31, 35, 34, 38, 31, 23, 24, 34, 36, 29, 32, 38, 27, 22, 29, 20, 40,

1.

Calculate r1, r2, ….., r10 and plot the correlogram.

Insert math as
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