xamine the following functions for maxima and minima:
a)
b)
For function ( z = -x^2 + xy - y^2 + x + 5y ), we first find the partial derivatives: [ \frac{\partial z}{\partial x} = -2x + y + 1, \quad \frac{\partial z}{\partial y} = x - 2y + 5 ] Setting them equal to zero: [ -2x + y + 1 = 0 \quad \Rightarrow \quad y = 2x - 1 ] [ x - __________ _____ _________ __________ _____ ____.
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(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)=x^0.7y^0.3. The consumer income is I=200 and p x=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)
Riemann Sum
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
B)/ C] = P(A/C) + P (B/C)
xamine the following functions for maxima and minima:
a)
b)
Using Simplex method solve the problem:
Maximise z = 4x + 8y + 2k
Subject to:
Also, minimize the same for z
Discuss the nature of the following time path:
b) Solve equation: for
) Russell's Paradox