business intelligence 6

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 , Fall 2018

Name: __________________________________________

Question 1.

a. Maximum profit attainable = $ …………………..[]

b. Number of gallons of each solvent used to produce each type of coolant []

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.

Part a. Rules obtained:

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.

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