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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.
Measures Of Skewness - These are numerical values such assist in evaluating the degree of deviation of a frequency distribution from the general distribution. - Given are t
pythagoras theorem
I have a simple right angle triangle. All I am given is h (the hypotenuse) and that ratio of x:y is 2:3. What is the formula to find x and y in terms of h?
We have seen that if y is a function of x, then for each given value of x, we can determine uniquely the value of y as per the functional relationship. For some f
2(x+3x)+(x+3x)
THINKING MATHEMATICALLY : Have you ever thought of what mental processes you are going through when you are solving a mathematical problem? Why don't you try the following proble
Ask question #Minimum 5 to 6 page accepted#
How many relations are possible from a set A of 'm' elements to another set B of 'n' elements? Ans: A relation R from a set A to other set B is specified as any subset of A
a man buy car at rs.50 and sells it at gain of 14% find the sp
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