MMIS 671: Fundamentals of Analytics and Business Intelligence
Final Exam, Fall 2018
Due by 9 am on Tuesday, December 4, 2018
Maximum Score: 35 Points.
Name: ________________________________________
· Please answer the questions and submit a single consolidated document by the due date.
· Late penalty 20 points
· You may use any reference material, but there should be no collaboration or consultations.
· Penalty for any collaboration 30 points
· The last 4 pages specify the format for presenting your solutions.
· Please let me know in class on November 27 if you need any clarifications.
Problem 1. Optimization Models [10 Points]
A company produces and sells two types of coolants (C1 and C2) by mixing three grades of solvents (A, B, and C) in different proportions.
Minimum percentages of grade A solvent and maximum percentages of grade C solvent allowed for each type of coolant are specified. The company has to produce at least a specified minimum quantity of each type of coolant. The table below presents these requirements, along with the selling price of each type of coolant.
Minimum percent of
grade A allowed |
Maximum percent of
grade C allowed |
Minimum Quantity Required
(gallons) |
Selling price
per gallon |
|
C1 | 40% | 30% | 100,000 | $4 |
C2 | 20% | 60% | 100,000 | $3 |
Availability of the three grades of solvents and their costs are as follows:
Grade | A | B | C |
Maximum quantity available per day (gallons) | 60,000 | 60,000 | 90,000 |
Cost per gallon | $3 | $2 | $1 |
The company wants to maximize profits subject to the specified constraints.
Formulate the problem as a linear program, find the optimal solution, and answer the following questions:
a. What is the maximum profit attainable? [3 Points]
b. How many gallons of each solvent are used to produce each type of coolant under the optimal solution? [3 points]
c. At most how much should the company be willing to pay for one additional gallon of grade A solvent (beyond its current availability of 60,000 gallons)? [4 points]
Problem 2. Linear Regression [10 Points]
The data file “trainFinal.csv” contains observations on 12 variables: class, x1, x2, …, x10, y
Run a regression to predict the output variable y based on the 10 input variables x1, x2, …, x10.
(a) [5 Points]
Interpret the regression results to complete the table below. Specify the coefficient estimates (rounded to 2 decimal places) under the column “Coefficient Estimate”. Specify whether the coefficient estimates are significant (Yes or No) at the 0.1% level under the column “Significant”
Coefficient Estimate | Significant? | |
Intercept | ||
x1 | ||
x2 | ||
x3 | ||
x4 | ||
x5 | ||
x6 | ||
x7 | ||
x8 | ||
x9 | ||
x10 |
(b) [5 Points]
Predict the expected value of y for the 10 examples in the data file “newFinal.csv” and report the predicted values (rounded to 1 decimal place) in the table below.
x1 | x2 | x3 | x4 | x5 | x6 | x7 | x8 | x9 | x10 | y |
0.36 | 0.30 | 0.68 | 0.38 | 0.02 | 0.61 | 0.53 | 0.52 | 0.35 | 0.78 | |
0.23 | 0.79 | 0.59 | 0.53 | 0.77 | 0.07 | 0.90 | 0.37 | 0.18 | 0.34 | |
0.80 | 0.96 | 0.35 | 0.69 | 0.19 | 0.59 | 0.85 | 0.55 | 0.75 | 0.68 | |
0.56 | 0.48 | 0.80 | 0.85 | 0.50 | 0.23 | 0.22 | 0.65 | 0.84 | 0.31 | |
0.75 | 0.39 | 0.47 | 0.02 | 0.19 | 0.23 | 0.99 | 0.03 | 0.65 | 0.87 | |
0.55 | 0.44 | 0.62 | 0.09 | 0.53 | 0.45 | 0.91 | 0.52 | 0.33 | 0.62 | |
0.20 | 0.70 | 0.24 | 0.81 | 0.22 | 0.01 | 0.82 | 0.67 | 0.40 | 0.46 | |
0.68 | 1.00 | 0.00 | 0.86 | 0.06 | 0.63 | 0.47 | 0.45 | 0.03 | 0.30 | |
0.08 | 0.49 | 0.97 | 0.08 | 0.68 | 0.82 | 0.89 | 0.82 | 0.47 | 0.96 | |
0.27 | 0.33 | 0.69 | 0.77 | 0.26 | 0.52 | 0.23 | 0.23 | 0.50 | 0.34 |
Problem 3. Classification Tree Inductive Learning [10 Points]
Train a decision tree classifier using the observations from the data file “trainFinal.csv” to classify the output binary variable “class” based on the 10 input variables: x1, x2, …, x10.
(a) [4 Points]
Specify the rules obtained in the form:
IF <Condition> Then class = ?
(b) [3 Points]
Use the rules obtained to predict the output class for the observations in data file “testFinal.csv” and present your confusion matrix.
actual | ||
predicted | 0 | 1 |
0 | ||
1 |
(c) [3 Points]
Use the rules obtained to predict the output class for the 10 observations in data file “newFinal.csv” and present your confusion matrix. [
x1 | x2 | x3 | x4 | x5 | x6 | x7 | x8 | x9 | x10 | class |
0.36 | 0.30 | 0.68 | 0.38 | 0.02 | 0.61 | 0.53 | 0.52 | 0.35 | 0.78 | |
0.23 | 0.79 | 0.59 | 0.53 | 0.77 | 0.07 | 0.90 | 0.37 | 0.18 | 0.34 | |
0.80 | 0.96 | 0.35 | 0.69 | 0.19 | 0.59 | 0.85 | 0.55 | 0.75 | 0.68 | |
0.56 | 0.48 | 0.80 | 0.85 | 0.50 | 0.23 | 0.22 | 0.65 | 0.84 | 0.31 | |
0.75 | 0.39 | 0.47 | 0.02 | 0.19 | 0.23 | 0.99 | 0.03 | 0.65 | 0.87 | |
0.55 | 0.44 | 0.62 | 0.09 | 0.53 | 0.45 | 0.91 | 0.52 | 0.33 | 0.62 | |
0.20 | 0.70 | 0.24 | 0.81 | 0.22 | 0.01 | 0.82 | 0.67 | 0.40 | 0.46 | |
0.68 | 1.00 | 0.00 | 0.86 | 0.06 | 0.63 | 0.47 | 0.45 | 0.03 | 0.30 | |
0.08 | 0.49 | 0.97 | 0.08 | 0.68 | 0.82 | 0.89 | 0.82 | 0.47 | 0.96 | |
0.27 | 0.33 | 0.69 | 0.77 | 0.26 | 0.52 | 0.23 | 0.23 | 0.50 | 0.34 |
MMIS 671: Fundamentals of Analytics and Business Intelligence
Solutions to Final Exam, Fall 2018
Name: __________________________________________
The work presented strictly reflects my individual efforts
Question 1.
a. Maximum profit attainable = $ …………………..[3 Points]
b. Number of gallons of each solvent used to produce each type of coolant [3 points]
Number of gallons used in: | grade A | grade B | grade C |
C1 | |||
C2 |
c. The company should be willing to pay at most $ ……………. for one additional gallon of grade A solvent (beyond its current availability of 60,000 gallons). [4 points]
Question 2.
Part a.
Coefficient Estimate | Significant? | |
Intercept | ||
x1 | ||
x2 | ||
x3 | ||
x4 | ||
x5 | ||
x6 | ||
x7 | ||
x8 | ||
x9 | ||
x10 |
Part b.
x1 | x2 | x3 | x4 | x5 | x6 | x7 | x8 | x9 | x10 | y |
0.36 | 0.30 | 0.68 | 0.38 | 0.02 | 0.61 | 0.53 | 0.52 | 0.35 | 0.78 | |
0.23 | 0.79 | 0.59 | 0.53 | 0.77 | 0.07 | 0.90 | 0.37 | 0.18 | 0.34 | |
0.80 | 0.96 | 0.35 | 0.69 | 0.19 | 0.59 | 0.85 | 0.55 | 0.75 | 0.68 | |
0.56 | 0.48 | 0.80 | 0.85 | 0.50 | 0.23 | 0.22 | 0.65 | 0.84 | 0.31 | |
0.75 | 0.39 | 0.47 | 0.02 | 0.19 | 0.23 | 0.99 | 0.03 | 0.65 | 0.87 | |
0.55 | 0.44 | 0.62 | 0.09 | 0.53 | 0.45 | 0.91 | 0.52 | 0.33 | 0.62 | |
0.20 | 0.70 | 0.24 | 0.81 | 0.22 | 0.01 | 0.82 | 0.67 | 0.40 | 0.46 | |
0.68 | 1.00 | 0.00 | 0.86 | 0.06 | 0.63 | 0.47 | 0.45 | 0.03 | 0.30 | |
0.08 | 0.49 | 0.97 | 0.08 | 0.68 | 0.82 | 0.89 | 0.82 | 0.47 | 0.96 | |
0.27 | 0.33 | 0.69 | 0.77 | 0.26 | 0.52 | 0.23 | 0.23 | 0.50 | 0.34 |
Question 3.
Rule 1.
Rule 2.
Rule 3.
….
….
Part b. | actual | |
predicted | 0 | 1 |
0 | ||
1 |
Part c.
Predicted class
x1 | x2 | x3 | x4 | x5 | x6 | x7 | x8 | x9 | x10 | Predicted class |
0.36 | 0.30 | 0.68 | 0.38 | 0.02 | 0.61 | 0.53 | 0.52 | 0.35 | 0.78 | |
0.23 | 0.79 | 0.59 | 0.53 | 0.77 | 0.07 | 0.90 | 0.37 | 0.18 | 0.34 | |
0.80 | 0.96 | 0.35 | 0.69 | 0.19 | 0.59 | 0.85 | 0.55 | 0.75 | 0.68 | |
0.56 | 0.48 | 0.80 | 0.85 | 0.50 | 0.23 | 0.22 | 0.65 | 0.84 | 0.31 | |
0.75 | 0.39 | 0.47 | 0.02 | 0.19 | 0.23 | 0.99 | 0.03 | 0.65 | 0.87 | |
0.55 | 0.44 | 0.62 | 0.09 | 0.53 | 0.45 | 0.91 | 0.52 | 0.33 | 0.62 | |
0.20 | 0.70 | 0.24 | 0.81 | 0.22 | 0.01 | 0.82 | 0.67 | 0.40 | 0.46 | |
0.68 | 1.00 | 0.00 | 0.86 | 0.06 | 0.63 | 0.47 | 0.45 | 0.03 | 0.30 | |
0.08 | 0.49 | 0.97 | 0.08 | 0.68 | 0.82 | 0.89 | 0.82 | 0.47 | 0.96 | |
0.27 | 0.33 | 0.69 | 0.77 | 0.26 | 0.52 | 0.23 | 0.23 | 0.50 | 0.34 |
Explanations for Question 1.
Explanations for Question 2.
Explanations for Question 3.
8
Final Exam, MMIS 671, Fall 2018
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