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Problem 1. Find the maximum and the minimum distance from the origin to the ellipse
x2 + xy + y2 = 3.
Hints: (i) Use x2 + y2 as your objective function; (ii) You can assume that the constraint qualification condition and the second order conditions are satisfied in this problem, as well as in problems 2 and 3.
Problem 2. Maximize f (x, y, z) = yz + xz subject to y2 + z2 = 1 and xz = 3.
Problem 3. (a) Maximize f (x, y) = x2 + y2 subject to 2x + y ≤ 2, x ≥ 0 and y ≥ 0.
(b) Use the Envelope Theorem to estimate the maximal value of the objective function in part
(a) when the first constraint is changed to 2x+ 9/8y ≤ 2, the second constraint is changed to x ≥ 0.1,and the third to y ≥ -0.1.
Given a standard 2x3 matrix show the ideal formed by the 2x2 minors is Prime.
2-3+=3+-4
A circle is inscribed in a triangle ABC having sides 8cm, 10cm and 12cm as shown in the figure. Find AD, BE and CF.
At times we consider only the magnitude of the number without attaching much importance to its direction. Under these circumstances the sign attached with the num
Rank Correlation Coefficient Also identified as the spearman rank correlation coefficient, its reasons is to establish whether there is any form of association among two vari
Give some children around you a task in mathematics. The task should be in an area in which they' have not been given a large dose of algorithms and strategies. Do all of them foll
You are required to implement Kruskal's algorithm for finding a Minimum Spanning Tree of Graph. This will require implementing : A Graph Data Type (including a display meth
WHATS HALVE OF 21
please can you help me with word problems
Find out the length of Hamiltonian Path in a connected graph of n vertices. Ans: The length of Hamiltonian Path in a connected graph of n vertices is n-1.
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