Reference no: EM132405433

DATA MINING

Question 1 Write a python program to classify IRIS dataset. Use libraries as
• NumPy
• Pandas
• Scikit Learn

Question 2 Write a python program to predict Boston Housing Price using Scikit Learn Plot the data and the regression line

Question 3 Write the algorithm to build a decision tree. You can use entropy measure.
Build the decision tree on IRIS Dataset

Question 4 Use python, to measure the accuracy of the models built in Q1,2,3.

STATISTICS FOR BUSINESS

Use dataset attached do the following tasks:
i) Find the measures of descriptive statistics for all the variables available in the dataset and comment about your findings about the nature of the distribution of those variables.
ii) Find the correlation between numeric variables and comment about strength of relationship between them.
Is correlationa measure of linear relationship? If yes, give a counter example to justify your claim.
iii) Use scatterplot to show relation between the variables you find useful for comparison.
iv) Use boxplot to comment about the nature of distribution of different variables.

DATA VISUALISATION

A case is being herewith being enclosed pertaining to online advertisement strategy to boost sales of a product.

The data associated with the product contains various information about online campaign and its effect on sales and cost.

You need to present the pertinent information such that a clear picture emerges from the information.

Marks:
1. Presenting the issue
2. Presentation of information pertaining to advertisement & sales
3. Presentation of information pertaining to Revenue and profit
4. Conclusion

Operations Research

Question 1. Illustrate the following:
a. Symmetric and skew-symmetric matrix
b. Linear Dependence and Independence
c. Eigen Values and Eigen Vectors
d. Condition of Inverse and Determinant of a matrix

Question 2. There is a marketing analysis of three products with three competitors and it has the following information: A purchases 4 units of Z and sells 3 units of X and 5 units of Y; B purchases 3 units of Y and sells 2 units of X and 1 unit Z; and C purchases 1 unit of X and sells 4 units of Y and 6 units of Z. In this process, A, B, and C earn $6000, $5000 and $13000 respectively. Using matrix algebra, find out the prices per unit of commodity.

Question 3. A company makes two products (X and Y) using two machines (A and B). Each unit of X requires 50 minutes processing time on machine A and 30 minutes processing time on machine B. Each unit of Y requires 24 minutes processing time on machine A and 33 minutes processing time on machine B. At the start of the current week there are 30 units of X and 90 units of Y in stock. Available processing time on machine A is forecasted to be 40 hours and on machine B is forecasted to be 35 hours. The demand for X in the current week is forecasted to be 75 units and for Y is forecasted to be 95 units. Company policy is to maximize the combined sum of the units of X and the units of Y in stock at the end of the week. Formulate the problem of deciding how much of each product to make in the current week as a linear program. Solve this linear program graphically.

Question 4. A carpenter makes tables and chairs. Each table can be sold for a profit of £30 and each chair for a profit of £10. The carpenter can afford to spend up to 40 hours per week working and takes six hours to make a table and three hours to make a chair. Customer demand requires that he makes at least three times as many chairs as tables. Tables take up four times as much storage space  as chairs and there is room for at most four tables each week. Formulate this problem as a linear programming problem and solve it graphically.

Question 5.
a. What is a standard form of Linear Programming Problem? What is the condition of moving from Graphical method of solution of LP to Simplex method?
b. Write down the assumptions of linear programming problem and explain in brief.
c. What is the significance of finding the dual of a primal linear programming problem?
d. Explain the difference between primal simplex and dual simplex method.
e. What is the condition of getting alternative solution and infeasible solution in - (i) primal simplex, (ii) dual simplex?

Question 6. Explain the algorithm of Two phase method of primal simplex in detail and then, solve the following problem:

A manufacturer produces three models of bicycles. The time (in hours) required for assembling, painting, and packaging each model is as follows.

	Model A	Model B	Model C
Assembling	2	2.5	3
Painting	1.5	2	1
Packaging	1	0.75	1.25

The total time available for assembling, painting, and packaging is 4006 hours, 2495 hours and 1500 hours, respectively. The profit per unit for each model is $45 (Model A), $50 (Model B), and $55 (Model C). How many of each type should be produced to obtain a maximum profit?

Question 7. Solve the following linear programming problem, first graphically and then by simplex algorithm.

Minimize cost = 4x1 + 5x2 , subject to: x1 + 2x2 ≥ 80, 3x1 + x2 ≥ 75, x1 , x2 ≥ 0

What are the values of the basic variables at each iteration? Which are the non-basic variables at each iteration?

Question 8. Find the dual of the following problem:

min 2x₁ + 15x₂ + 5x₃ +6x₄
s.t x₁ + 6x₂ + 3x₃ + x₄ > 2
-2x₁ + 5x₂ - x₃ + 3x₄ < -3
x₁, x₂, x₃, x₄ > 0

Attachment:- EPGDM in Business Analytics.zip