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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.
Al is painting a right cylinder storage tank. In sequence to purchase the correct amount of paint he requires to know the total surface area to be painted. Which formula will he us
if area of a rectangle is 27 sqmtr and it perimeter is 24 m find the length and breath#
Q. How to calculate Percentiles? Ans. In a large group of standardized test scores we expect the scores to approximate a normal curve. If all scores are translated to z-s
sin45
Explain Introduction to Non-Euclidean Geometry? Up to this point, the type of geometry we have been studying is known as Euclidean geometry. It is based on the studies of the a
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