MEC-003/103 Solved Assignment 2018-19 (Quantitative Methods)

Description

Course Code :	MEC-3/103
Course Title :	Quantitative Methods
Assignment Code :	MEC-003/103/AST/2018-19
Maximum Marks :	100
Weightage :	30%
Last date of Submission :	31 March, 2019 (for July 2018 Session) 30 September, 2019 (for January 2019 Session)

Note: Answer all the questions. While questions in Section A carry 20 marks each (to be answered in about 700 words each) those in Section B carry 12 marks each (to be answered in about 500 words each).

SECTION-A

1. a) What is a first order differential equation? When would you like to use this equation? List the steps you would follow to find solution for homogenous and non-homogenous differential equations.

b) Find general and particular solution of the following equation

??/??+10?=15 ; ?(0)=0

2. Under perfect competition a firm produces two commodities A and B and their given prices are P₁ = 5 and P₂ = 3, respectively. Accordingly, the firm’s revenue function R= 5q₁+3q₂. Where q₁ and q₂ representthe quantity of output of the two products, respectively. The firm’s cost function is C = 2q₁² + 2 q₂²+ q₁q₂. Find the profit maximizing output and Hessian matrix. Also draw your conclusion from the Hessian matrix.

SECTION-B 

3. a) State the Hawkins-Simon conditions in the context of input-output analysis.

b) Suppose the technology matrix is
|A| =

0.2	-0.2
-0.9	0.3

Find whether any solution is possible for the underlying system or not.

4. From the following data, obtain the two regression equations Y on X and X on Y

X	2	4	6	8	10
Y	5	7	9	8	11

5. If ?̅is the sample mean, prove that the expected value of?̅,that isE(?̅), equals the population mean (μ)

6. What is the difference between probability density function (PDF) and Probability mass function (PMF)? Write down the properties they must satisfy.

7. Solve the following linear programing problem model in x₁ and x₂:
Maximize Z = 5x₁ + 10x₂
Subject to x₁ + 3x₂ ≤ 50
4x₁ + 2x₂ ≤ 60
x₁ ≤ 5
x₁ , x₂ ≥0