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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Chi square test of goodness of fit
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)
Riemann Sum
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.
Maximin or Minimax Principle
Discuss the nature of the following time path:
b) Solve equation: for
Using Simplex method solve the problem:
Maximise z = 4x + 8y + 2k
Subject to:
Also, minimize the same for z