1. Students in a management science class have just received their grades on the first test. The instructor has provided information about the first test grades ( ) in some previous classes as well as the final average ( ) for the same students. Some of these grades have been sampled and are as follows:

Students

A

B

C

D

E

F

First Test Grade (x)

97

77

88

80

95

61

Final average (y)

92

78

83

73

84

64

a. Develop a regression model that could be used to predict the final average in the course based on the first test grade.

b. Predict the final average of a student who made an 83 on the first test.

2. Using the data in problem-1, compute the SST, SSE, SSR and r2 with the help of QM for windows. Interpret the value of r2 in context of this problem.

You can download QM for windows from the following link.

(http://wps.prenhall.com/bp_taylor_introms_11/220/56508/14466195.cw/content/).

3. A university cafeteria line in the student center is a self-serve facility in which students select the food items they want and they form a single line to pay the cashier. Student arrive at cashier at the rate of about four per minute according to a Possion distribution. The single cashier ringing up sales takes about 12 seconds per customers, following an exponential distribution.

a. What is the probability that the system is empty?

b. What is the expected number of student in the queue?

c. How long will the average student have to wait before reaching the cashier?

4. Automobiles arrive at the drive-through window at post office at the rate of 4 every 10 minutes. The average service time is 2 minutes. The Poisson distribution is appropriate for the arrival rate and service time are exponentially distributed.

a. What is the average time a car in the system?

b. What is the average time a car spend waiting to receive service?

c. What is the average number of car in the system?

5. The Saudi Furniture Corporation manufactures two products, chairs and tables. The firm has two resources: its carpenters (Labor force) and a supply of redwood for use in the furniture. In the next production cycle, 1,200 hours of labor are available under the agreement. The firm also has a stock of 3,500 board feet of good-quality redwood. Each chair requires 4 labor hours and 10 board feet of redwood: each table takes 6 labor hours and 35 board feet of redwood. Completed chairs will yield a profit of $9 each, and tables will result in a profit of $20 each. Formulate the LPP for largest profit from the combination of chair and table that Saudi Furniture Corporation manufactures can produce.

6. Solve the following LPP using the corner point graphical method.

Subject to