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**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 ofgrade A allowed | Maximum percent ofgrade C allowed | Minimum Quantity Required(gallons) | Selling priceper 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**