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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.
Determine the fundamental period of the following discrete-time signal: X(n) = 2sin(4n)π +π/4) + 5sin16n +4sin (20n +π/3)
i want aasignment on this topic
robin runs 5 kilometers around the campus in the same length of time as he can walk 3 kilometers from his house to school. If he runs 4 kilometers per hour faster than he walks, ho
Determine the mean of the subsequent numbers: Example: Determine the mean of the subsequent numbers: 5, 7, 1, 3, 4 Solution: where x' =
Q. Probability of Independent Events? Ans. Consider these two events: {My name is Shirley} {The rain is falling} Are these events related to each other? No. My name
how can i evaluate this lim of x as x approaches to a
Let D = 1 denotes the event that an adult male has a particular disease. In the population, it is known that the probability of having this disease is 20 percent, i.e., Pr (D = 1)
what is 3/2 - 1/2
There are 81 women teachers at Russell High. If 45% of the teachers in the school are women, how many teachers are there at Russell High? Use the proportion part/whole = %/100.
Area of the equilateral triangle: Given : D, E, F are the mind points of BC, CA, AB. R.T.P. : We have to determine the ratio of the area of of triangle DEF and triangle AB
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