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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.
If ABCD isaa square of side 6 cm find area of shaded region
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For each of these arguments determine whether the argument is correct or incorrect and explain why. a) Everyone enrolled in the university has lived in a dormitory. Mia has never l
Do you have to pay.
Using the sketch below and the fact that ∠A + ∠B + ∠C + ∠D = 325, Determine m∠E. a. 81° b. 35° c. 25° d. 75° b. The addition of the measures of the exterio
show that a*0=a
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