# MMIS 671: Fundamentals of Analytics and Business Intelligence Final Exam, Fall 2015

**MMIS 671: Fundamentals of Analytics and Business Intelligence**

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**Final Exam, Fall 2015**

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**Maximum Score: 35 Points.**

**Due by 11:59 p.m. on Monday, December 7.**

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**Name: ________________________________________**

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**Please answer the questions and submit a single consolidated document.****Late penalty 20 points****You may use any reference material, but there should be no collaboration or consultations.****Penalty for any collaboration 30 points**

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**Problem 1. Optimization Models [15 Points]**

A company produces three types of products – *P1*, *P2*, and *P3*. Because of limited demands, it is constrained toproduce no more than a specified quantity of these products. Three types of raw materials – *RM1*, *RM2*, and *RM3* are required for the manufacturing process.

The table below summarizes the relevant data. The profits resulting from each unit of *P1*, *P2*, and *P3* are $6, $8, and $10, respectively. The maximum quantities of *P1*, *P2*, and *P3* that the company can produce are 3000 units, 2000 units, and 1500 units, respectively. The availability for raw materials *RM1*, *RM2*, and *RM3* are 18000 units, 30000 units, and 36000 units, respectively. The resource requirements for each product may be interpreted as follows:

It takes 2 units of *RM1*, 4 units of *RM2*, and 5 units of *RM3* to produce each unit of *P1*.

It takes 4 units of *RM1*, 5 units of *RM2*, and 6 units of *RM3* to produce each unit of *P2*.

It takes 5 units of *RM1*, 8 units of *RM2*, and 10 units of *RM3* to produce each unit of *P3*.

| P1 | P2 | P3 | Available |

RM1 | 2 | 4 | 5 | 18000 |

RM2 | 4 | 5 | 8 | 30000 |

RM3 | 5 | 6 | 10 | 36000 |

Demand | 3000 | 2000 | 1500 | |

Profit/unit | $ 6 | $ 8 | $ 10 |

Formulate this problem as a linear program and obtain the optimal solutions so as to maximize the total profits under the given constraints.

Answer the following questions:

- What is the maximumprofit attainable? [3 Points]

- How many units of
*P1*,*P2*, and*P3*are produced under the optimal plan? [3 Points]

- How many units of
*RM1*,*RM2*, and*RM3*are used under the optimal plan? [3 Points]

- How much should the company be willing to pay for an additional unit of
*RM1*? [2 Points]

- How much should the company be willing to pay for an additional unit of
*RM2*? [2 Points]

- How much should the company be willing to pay for an additional unit of
*RM3*? [2 Points]

**Problem 2. Linear Regression [10 Points]**

The data file “FinalTrain.csv” contains 750 observations of 6 variables: “TEMP”, “FLOW”, “CONCENTRATION”, “CONTROL”, “HARDNESS”, and “QUALITY”.

Run a regression to predict the output variable “HARDNESS”based on the input variables “TEMP”, “FLOW”, “CONCENTRATION”, and “CONTROL”.

- [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) | ||

TEMP | ||

FLOW | ||

CONCENTRATION | ||

CONTROL |

- [5 Points]

Predict the expected value of HARDNESS for the first 5 records in the data file “FinalTest.csv” and report the predicted values (rounded to 1 decimal place) in the table below.

TEMP | FLOW | CONCENTRATION | CONTROL | HARDNESS |

316 | 1099 | 466 | 0 | |

304 | 1099 | 481 | 0 | |

299 | 1189 | 471 | 1 | |

382 | 1231 | 472 | 1 | |

247 | 1203 | 548 | 0 |

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**Problem 3. Decision Tree Inductive Learning [10 Points]**

Train a decision tree classifier using the 750 observations from the data file “FinalTrain.csv” to classify the output binary variable “QUALITY” based on the 4input variables: “TEMP”, “FLOW”, “CONCENTRATION”, and “CONTROL”.

- [5 Points]

Specify the rules obtained in the form:

IF <Condition> Then QUALITY = ?

- [5 Points]

Use the rules obtained to predict the output class for “QUALITY” for the 250 observations in data file “FinalTest.csv” and present your confusion matrix.

predicted | ||

actual | 0 | 1 |

0 | ||

1 |