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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.
Case 1: Suppose we are given expressions like 3abc and 7abc and asked to compute their sum. If this is the case we should not worry much. Because adding like exp
three complain forces of magnitudes 20N 30N and 45N
Andy earned the subsequent grades on his four math quizzes: 97, 78, 84, and 86. What is the average of his four quiz grades? To ?nd out the average, you must add the items (97
How do I choose a distribution test for a sample size of 60? Probability of rolling a 4 on a six sided die.
whats the best way to solpve
A telephone dialled is numbered 0to9. if 0is dialled first the caller is connected to the international exchange system.find the number of local calls that can be rung if a local n
write the equation of parabola of vertex(2,-3)and focus(_1,1)
what is the trignomatry ratio
Estimation of population proportions This form of estimation applies at the times while information cannot be described as a mean or as a measure but only as a percentage or fr
sinx
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