Description
MEC 103: QUANTITATIVE METHODS
Tutor Marked Assignment
Course Code: MEC-103
Assignment Code: Asst /TMA /2025-26
Total Marks: 100
SECTION A Answer the following questions. Each question carries 20 marks 2 × 20 = 40
1) (a) Explain the theorem of second order optimum.
(b) Consider the following utility maximization problem, in which the utility function of the consumer is given by U(x,y)=x0.7y0.
. The consumer income is I=200 and px=3 and py=
2.Find the utility maximizing x and y when the budget constraint of the consumer may or may not bind. (Apply Kuhn-Tucker method) 2) Given the input matrix and the final demand vector: 𝐴=[ 0.10 0.15 0.12 0.20 0 0.30 0.25 0.40 0.20 ]𝑑=[ 100 200 300 ] a) Explain the economic meaning of the elements 0.30,0 and 200 b) Explain the economic meaning of (if any) of the third column sum
c) Explain the economic meaning of (if any) of the third row sum d) Write out the specific input-output matrix equation for this model
e) Find the solution output levels of the three industries using Cramer’s rule.
SECTION B Answer the following questions. Each question carries 12 marks. 6 X 12=60
3) Using Simplex method solve the problem: Maximise 𝑧=4𝑥+8𝑦+2𝑘 Subject to: 1 2 𝑥+2𝑦+4𝑘≥4 � �+𝑦−2𝑘≥6 � �≥0,𝑦≥0,𝑘≥0 Also, minimize the same for z
4) a.) Ram and Rahim play for a prize of Rs. 99. The prize is to be won by the player who first throws a 3 with a single die. Ram throws first and if he fails Rahim throws it and if Rahim fails Ram throws it again and this process continues. Find their respective expectations.
b.) If P (A ∩ B∩ C) = 0, show that P [(A U B)/ C] = P(A/C) + P (B/C)
5) a) Discuss the nature of the following time path: 𝑦𝑡=3𝑡+1
b) Solve equation: 𝑦𝑡+1−1 3 𝑦𝑡=6 𝑓𝑜𝑟 𝑦0=1
6) Examine the following functions for maxima and minima:
a) 𝑧=−𝑥2+𝑥𝑦−𝑦2+𝑥+5𝑦 b) 𝑦=𝑥3−2𝑥2+𝑥−6
7) Write short notes on following:
a) Maximin or Minimax Principle b) Riemann Sum c) Russell’s Paradox d) Chi square test of goodness of fit
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