business intelligence 6
Roz
SampleassiBI5.docxMMIS 671: Fundamentals of Analytics and Business Intelligence
Sample, Fall 2018
Problem 1. Optimization Models []
A company produces three types of products – P1, P2, and P3. Because of limited demands, it is constrained to produce 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 cost per unit of RM1, RM2, and RM3 are $3, $4, and $2, 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 |
Cost per unit |
|
RM1 |
2 |
4 |
5 |
18000 |
$3 |
|
RM2 |
4 |
5 |
8 |
30000 |
$4 |
|
RM3 |
5 |
6 |
10 |
36000 |
$2 |
|
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:
(a) What is the maximum profit attainable? [3 Points]
(b) How many units of P1, P2, and P3 are produced under the optimal plan? [3 Points]
(c) How many units of RM1, RM2, and RM3 are used under the optimal plan? [3 Points]
(d) How much should the company be willing to pay for an additional unit of RM1? [2 Points]
(e) How much should the company be willing to pay for an additional unit of RM2? [2 Points]
(f) How much should the company be willing to pay for an additional unit of RM3? [2 Points]
Problem 2. Linear Regression []
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".
(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) |
|
|
|
TEMP |
|
|
|
FLOW |
|
|
|
CONCENTRATION |
|
|
|
CONTROL |
|
|
(b) [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 |
|
Problem 3. Decision Tree Inductive Learning []
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 4 input variables: "TEMP", "FLOW", "CONCENTRATION", and "CONTROL ".
(a) [5 Points]
Specify the rules obtained in the form:
IF <Condition> Then QUALITY = ?
(b) [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.
|
|
actual |
|
|
predicted |
0 |
1 |
|
0 |
|
|
|
1 |
|
|
Solutions. Name: __________________________________________
Question 1.
|
a |
Maximum Profit = |
$ |
|
b |
Number of units of P1 produced = Number of units of P2 produced = Number of units of P3 produced = |
units units units |
|
c |
Number of units of RM1 used = Number of units of RM2 used = Number of units of RM3 used = |
units units units |
|
d |
Maximum amount for an additional unit of RM1= |
$ |
|
e |
Maximum amount for an additional unit of RM2= |
$ |
|
f |
Maximum amount for an additional unit of RM3= |
$ |
Question 2.
|
Part a. |
Coefficient Estimate |
Significant (Yes/No)? |
|
(Intercept) |
|
|
|
TEMP |
|
|
|
FLOW |
|
|
|
CONCENTRATION |
|
|
|
CONTROL |
|
|
Part b.
|
TEMP |
FLOW |
CONCENTRATION |
CONTROL |
HARDNESS (predicted) |
|
316 |
1099 |
466 |
0 |
|
|
304 |
1099 |
481 |
0 |
|
|
299 |
1189 |
471 |
1 |
|
|
382 |
1231 |
472 |
1 |
|
|
247 |
1203 |
548 |
0 |
|
Question 3.
Part a. Rules obtained:
Rule 1.
Rule 2.
Rule 3.
….
….
|
Part b. |
actual |
|
|
predicted |
0 |
1 |
|
0 |
|
|
|
1 |
|
|
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