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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.
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Also, their inability to apply the algorithm for division becomes quite evident. The reason for these difficulties may be many. We have listed some of them below. 1) There are n
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You know the experation for the area of a circle of radius R. It is Pi*R 2 . But what about the formula for the area of an ellipse of semi-minor axis of length A and semi-major
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Two people are 50 feet separately. One of them begin walking north at rate so that the angle illustrated in the diagram below is changing at constant rate of 0.01 rad/min. At what
A certain flight arrives on time 78% of the time. Suppose 1000 flights are randomly selected. Use the normal approximation to the binomial to approximate the probability that a)
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