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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.
parts of matrix and functions
Impediments in time series analysis Accuracy of data in reflecting a) Drastic changes for illustration in the advent of a major competitor, period of war or unexpected chan
6987+746-212*7665
To find out the perimeter of a triangular region, what formula would you use? The perimeter of a triangle is length of surface a plus length of side b plus length of side c.
Solve for x: 4 log x = log (15 x 2 + 16) Solution: x 4 - 15 x 2 - 16 = 0 (x 2 + 1)(x 2 - 16) = 0 x = ± 4 But log x is
Indefinite Integrals : In the past two chapters we've been given a function, f ( x ) , and asking what the derivative of this function was. Beginning with this section we are now
Interpretations of the Derivative : Before moving on to the section where we study how to calculate derivatives by ignoring the limits we were evaluating in the earlier secti
how to find the indicated term?
A building is in the form of a cylinder surrounded by a hemispherical vaulted dome and contains 41(19/21-) cu m of air. If the internal diameter of the building is equal to its t
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