Section-I
State whether the following statements are True or False. (5X1=5 Marks)
1. In regression equations represented by Y = 2 + 3X, if value X =2 then predicted value of Y is 10.
2. Residual = Actual Value - Predicted Value
3. In a queuing system, percentage of time a server is busy is called the utilization factor for the system.
4. In a constant service time model, both the average queue length and average waiting time are halved.
5. In a linear program, the constraints must be linear, but the objective function may be nonlinear.
Section-II
Circle the right answer from the answers given below. (5X1=5 Marks)
1. If computing a causal linear regression model of Y = a + bX and the resultant r2 is very near zero, then one would be able to conclude that
A) Y = a + bX is a good forecasting method.
B) Y = a + bX is not a good forecasting method.
C) a multiple linear regression model is a good forecasting method for the data.
D) a multiple linear regression model is not a good forecasting method for the data.
2. The correlation coefficient resulting from a particular regression analysis was 0.25. What was the coefficient of determination?
A) 0.5
B) -0.5
C) 0.0625
D) There is insufficient information to answer the question.
3. Which of the following is not a valid queuing model based on the Kendall notation?
A) M/M/3
B) D/D/2
C) D/M/1
D) M/M/0
4. Customers enter the waiting line to pay for food as they leave a cafeteria on a first-come, first-served basis. The arrival rate follows a Poisson distribution, while service times follow an exponential distribution. If the average number of arrivals is 4 per minute and the average service rate of a single server is 7 per minute, what proportion of the time is the server busy?
A) 0.43
B) 0.57
C) 0.75
D) 0.25
5. Consider the following linear programming problem:
The feasible corner points are (48, 84), (0, 120), (0, 0), (90, 0). What is the maximum possible value for the objective function?
A) 1032
B) 1200
C) 360
D) 1600
Section-III
Answer the following Essay Type Questions (3X5 =5Marks)
1. An air conditioning and heating repair firm conducted a study to determine if the average outside temperature, thickness of the insulation, and age of the heating equipment could be used to predict the electric bill for a home during the winter months in Houston,
Texas. The resulting regression equation was:
Y = 256.89 - 1.45X1 - 11.26X2 + 6.10X3,
where Y = monthly cost, X1 = average temperature, X2 = insulation thickness, and X3 = age of heating equipment
(a) If December has an average temperature of 45 degrees and the heater is 2 years old with insulation that is 6 inches thick, what is the forecasted monthly electric bill?
(b) If January has an average temperature of 40 degrees and the heating equipment is 12 years old with insulation that is 2 inches thick, what is the forecasted monthly electric bill?
2. A local fast food restaurant has a drive thru operation that has a single server. Customers arrive, on average, every 5 minutes and can be served, on average, every 4minutes. The management has found that the arrival pattern follows the Poisson distribution while the service times tend to follow the exponential distribution. Assuming that the calling population size is infinite and the queue length is unrestricted, answer the following:
a. What is the server utilization?
b. The average time a customer spends waiting in the queue.
c. How many customers, on average, are waiting to be served?
d. How long does it take the average customer to move through the system (waiting plus service)?
e. How many customers, on average, are in the system at any given time?
3. Solve graphically the following 3 linear programming problems
Maximize (Z) =
subject to