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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.
a man in rested rupee 800 is buying rupee 5 shares and then are selling at premium of rupee 1.15. He sells all the shares.find profit
Write an octave program that will take a set of points {x k , f k } representing a function and compute the derivative at the same points x k using 1. 2-point forward di erence
Classical Probability Consider the experiment of tossing a single coin. Two outcomes are possible, viz. obtaining a head or obtaining a tail. The probability that it is a tail
Initial Condition(s) are a set of conditions, or a condition on the solution which will permit us to find out that solution which we are after. Initial conditions are frequently a
Marketing management,Analysis,planning and implementation
(x+y+1)dy/dx=1
a) Specify that a tree has at least 2 vertices of degree 1. b) What is the largest number of vertices in a graph with 35 edges if all vertices are
if I read 6 hours of spring break how many minutes did read
Why is tossing a coin considered to be a fair way of deciding which team should get the ball at the beginning of a foot ball match? Ans: equally likely because they are mutual
2/3 - 7/12
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