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1-Students in management science class have just received their grades on the fi

ID: 3129726 • Letter: 1

Question

1-Students in 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 follow:

1st test Grade

98

77

88

80

96

61

64

95

79

Final average

93

78

84

75

84

64

66

95

86

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

-Predict the final average of a students who made an 83 on the first test.

-Give the value of r and for this model. Interpret the value of in the context of this problem.

2-From historical data, Harry’s Car Wash estimates that dirty cars arrive at the rate of 8 cars per hour all day Saturday. With a crew working the wash line, harry figures that car can be cleaned at the rate of one every 6 minutes. One car at a time cleaned in this example of a single-channel waiting line. Assuming Poisson arrival and exponential service times, find the

Average number of cars in line.

Average time a car waits before it is washed.

Average time a car spends in the service system.

Utilization rate of the car wash.

Probability that no car are in the system.

3-Woofer Pet Food produces a low-calorie dog food for overweight dogs. This product is made from beef products and grain. Each pound of beef costs $0.80, and each pound of grain costs $0.50. A pound of the dog food must contain at least 10 units of Vitamin 1 and 12 units of Vitamin 2. A pound of beef contains 5 units of vitamin 1 and 7 units of vitamin 2. A pound of grain contains 6 units of vitamin 1 and 9 unites of vitamin 2. Formulate this as an LP problem to minimize the cost of the dog food. How many pounds of beef and grain should be included in each pound of dog food? What is the cost and vitamin content of final product?

1st test Grade

98

77

88

80

96

61

64

95

79

Final average

93

78

84

75

84

64

66

95

86

Explanation / Answer

Step 2: Find the sum of every column:

X=738 , Y=725 , XY=60523 , X2=61976

LIne is y = 20.291+0.735 x

y(83) = 81.296

r =0.9158

strong positive correlation between x and y

----------------------

2) Average cusomers = 60/6 = 10

12 min

X Y XY XX 98 93 9114 9604 77 78 6006 5929 88 84 7392 7744 80 75 6000 6400 96 84 8064 9216 61 64 3904 3721 64 66 4224 4096 95 95 9025 9025 79 86 6794 6241