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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.
how to solve temperature converting
Find and classify all the equilibrium solutions to the subsequent differential equation. y' = y 2 - y - 6 Solution First, get the equilibrium solutions. It is generally
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word problem
MATHEMATICS - IN OUR LIVES : What is the most obvious example of mathematics in your life? To many of us it is the maths that we studied in school. But is that all the mathemat
Find out the determinant: Find out the determinant of the following 3 x 3 matrix, expanding about row 1. Solution:
How many people ca fi in a small cars without seats?
As we saw in the previous section computing Laplace transforms directly can be quite complex. Generally we just utilize a table of transforms when actually calculating Laplace tran
Mathematical Formulae (a + b) 2 = a 2 + b 2 + 2ab (a - b) 2 = a 2 + b 2 - 2ab (a + b) 2 +
Find the normalized differential equation which has {x, xex} as its fundamental set
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