1. State whether the following statements are True or False. Give reasons in support of your answers.

The number of possible basic solutions in an LPP of order 2x3 is 5.

If there are 3 jobs to be performed, one at a time on each of the 2 machines, then the possible number of sequences would be 36.

If the average expenditure of 10 families is Rs 5,000, the average number of family members is 4 and the slope is 200.5 for a regression equation of monthly expenditure on the number of family members, then the value of the intercept wiii be 580.

A correlogram suggests that the observations with larger lag are positively correlated.

The average queue length of an queue is where 2 per minute is the arrival rate and 4 per minute is the service rate.

An electronic firm manufactures transistors, resistors and carbon tubes with a profit of Rs 10, Rs 6 and Rs respectively, for a shipment. To produce a shipment of transistors; 1 hour of engineering, 10 hours of direct labour and 2 hours of administrative services are required. To produce one shipment of resistors, 4 and 2 hours are required for engineering, direct labour and administrative services, respectively. To produce one shipment of tubes, 1 hour of engineering, 5 hours of direct labour and 6 hours of administrative services are required. There are 100 hours of engineering, 600 hours of direct labour and 300 hours of administrative services. What is the most profitable mix using the Simplex Method?
OR
A manufacturer has distribution centres at Y and Z. These centres have availability of 30, 25 and 35 writs of the product, respectively. His retail outlets at C and D require 20, 10, 20 and 40 Units, respectively. The transport cost (in Rs) per unit between each centre outlet is given below:

<img src='./qimages/10351-2b.jpg'>

Determine the optimal distribution to minimise the cost of transportation using Vogel and MODI methods.

A private firm employs typists on an hourly rate for their daily work. Five typists are working in that firm and their charges and speeds are different. Only one job is given to one typist. Find the least cost allocation
and minimum cost for the following data:

<img src='./qimages/10351-3a.jpg'>

A supermarket has a single cashier. During the peak hours, customers arrive at Iii rate of 20 customers per hour, The average number of customers that can be processed by the cashier is 24 per hour.

Calculate

The average number of customers in the system

Average waiting time of a customer in queue
OR
Seven jobs go first over Machine 1 and then over Machine 2. Processing times in hours are given as follows

<img src='./qimages/10351-3c.jpg'>

Find the optimum sequence in which the jobs should be processed. Also obtain the minimum elapsed time and the idle time for each machine.

The production department of a company requires 7200 kg of raw material for manufacturing a particular item per year. It has been estimated that the cost of placing an order is Rs 72 and the cost of carrying inventory is 25 percent of the cost of the inventory. The price is Rs 20 per kg. The purchase manager wishes to determine an ordering policy for raw material. Find the
economic lot size, number of orders placed per year, and total minimum cost.

The marketing manager of a large supermarket chain would like to use shelf space to predict the sales of pet food. A random sample of 12 equal sized stores is selected, with the following results

<img src='./qimages/10351-4a.jpg'>

Predict the weekly sales of the pet food for stores with 8 feet of shelf space for pet food.

Estimate the variance of error.

Is there any evidence of a linear relationship between shelf space and sales at level of significance?
OR
A firm conducted a study On its employees to examine the relationship between their personality and IQ. For this purpose, ten employees were selected and one IQ as well as two different personality tests were given to them. The results obtained on IQ level
test and test II(x2) are given below:

<img src='./qimages/10351-4b.jpg'>

Using the matrix method,

fit a multiple linear regression model.

compute the value of the coefficient of determination and interpret the result.

A company is interested in forecasting the demand for one of its products. the data on demand for the last 12 months ate given below:

<img src='./qimages/10351-5a.jpg'>

Forecast the demand for the 13th month using exponential smoothing technique for w=0·2.

Compute the 3-monthly moving average for this data.

Plot the demands obtained by 3-monthly moving average and exponential smoothing method along with the given data.
OR
Define Autoregressive process.

For the following Autoregressive model

xt O·7Xt-l O·4 Xt-2+at

Verify whether the series is stationary.

Obtain Pk 4 and 5.

Plot the correlogram.