State whether the following statements are True or False. (16=6) 1. The SSR indicates how much of the total variability in the dependent variable is explained by the regression model. 2. When we want to use one variable to predict another and use the equation: y = a + bx, we use the technique known as multiple regression. 3. The goal of most waiting line problems is to identify the service level that minimizes service cost. 4. A bank with a single queue to move customers to several tellers is an example of a singlechannel system. 5. A marketing research linear programming model can help a researcher structure the least expensive, statistically meaningful sample. 6. In a linear program, the constraints must be linear, but the objective function may be nonlinear. Section-II Circle/tick the right answer from the answers given below. (16=6) 1. The random error in a regression equation: A) is the predicted error. B) includes both positive and negative terms. C) will sum to a large positive number. D) is used the estimate the accuracy of the slope. 2. 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. 3. Which of the following distributions is most often used to estimate the arrival pattern? A) Negative exponential B) Normal C) Poisson D) Erlang 4. Which of the following is not a valid queuing model based on the Kendall notation? A) M/M/3 B) M/D/2 C) M/M/1 D) M/M/0 5. Which of the following is not a property of linear programs? A) One objective function B) At least two separate feasible regions C) Alternative courses of action D) One or more constraints 6. Using feasible corner points (0, 0), (90, 0) in following linear programming problem: 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 (63=18) 1. A new young businessman has opened a cloth diaper service. He is interested in forecast the demand of diapers required for a one-year- old infants the data given table below: Days (x) Demand (y) 1 10 2 9 a) Fit a regression line a) Forecast demand Y 3 11 Y b0 b1 X when 4 12 5 15 between days and demand. X 10 . 2. From the data given in following table (Y Y ) Y 7 2 SST = 22.5 (Y Y ) 22.5 2 6.875 SSE = 6.875 (a) Find Coefficient of Determination r2. (b) Find the value of correlation Coefficient . r (Y Y ) 2 15.625 SSR = 15.625 (c) Interpret the value of r 2 in the context of this problem. 3. In shopping center customers arrive at a sales counter managed by a single person randomly with a mean rate of 30 per hour. The time required to serve a customer has an exponential distribution with a mean of 120 seconds. (a) Find the average waiting time of a customer in the queue. (b) Find the average waiting time of a customer in the System. 4. The students patiently form a single line in front of the desk to wait for helpat State University has a help desk. Student arrivals are best described using a Poisson distribution with mean 10 students per hour arrive at the help desk. The help desk server can help an average of 20 students per hour, with the service rate being described by an exponential distribution. Calculate the following operating characteristics of the service system: (a) The average utilization of the help desk server (b) The average number of students in the system (c) The average number of students waiting in line 5. Two advertising media are being considered for promotion of a product. Website ads cost $80 each, while TV ads cost $120 each. The total budget is $960 per week. The total number of ads should be at least 10, with at least 3 of each type. Each TV ad reaches 1200 people, while each Website ad reaches 1,000 people. The company wishes to reach as many people as possible while meeting all the constraints stated. How many ads of each type should be placed? 6. Consider a product mix problem, where the decision involves determining the optimal production levels for products Prod1 and Prod2. A unit of Prod1 requires 2 hours of labor in department 1 and 4 hours a labor in department 2. A unit of Prod2 requires 5 hours of labor in department 1 and 7 hours of labor in department 2. Currently, 700 hours of labor time are available in department 1, and 900 hours of labor time are available in department2. Furthermore, 300 additional hours of cross-trained workers are available to assign to either department (or split between both). Each unit of Prod1 sold returns a $30 profit, while each unit of Prod1 sold returns a $40 profit. All units produced can be sold. Formulate this problem as a linear programming