MEC-203 Solved Assignment English Medium 2023-24

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MEC-203 Solved Assignment English Medium 2023-24

MEC-203: QUANTITATIVE METHODS
Tutor Marked Assignment
Course Code: MEC-203
Asst. Code: MEC-203/TMA/2023-24
Total Marks: 100
Note: Answer all the questions.
Questions in Section A carry 20 marks each (to be answered in about 500 words each)
Questions in Section B carry 12 marks each (to be answered in about 300 words each).
Word limits do not apply to the numerical questions.
Section A
1. a) Explain the necessary and sufficient conditions in case of unconstrained optimisation.
b) Consider a consumer who buys two goods, x and y with utility function u(x, y) = 2√x + y. The consumer’s income is 20 and price of y is 4. Compute the optimal consumption bundle when the price of x is equal to 1 using constrained optimisation. (10 + 10 = 20)
2. With respect to the applications of dynamic optimisation, explain the optimal rate of extraction of exhaustible resources by monopoly.
Section B
3. What is a discontinuous function? Discuss the two types of discontinuous functions along with their diagrams.
4. Explain the concept of a stationary point and inflexion point. Is a stationary point always a point of inflexion? Why or why not? (6 +6 =12)
5. What do you understand by the term ‘joint distribution’ and ‘marginal distribution’? Discuss with the help of an example.
6.What is a sample? Explain with the help of an example. Discuss any two types of sampling techniques. (6 + 6 = 12)
7) Write short notes on the following: (3 X 4 = 12)
(i) One-tailed and two-tailed tests
(ii) One to one and onto functions
(iii) Hyperbola
(iv) Local minima