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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.
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A man invest ?13500 partly in shares paying 6% at ?140 and partly in 5% at 125.If he is tolal income is 560, how much has he invested in each?
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a. Estimate the following model, C t = β 0 + β 1 * DI t + ε t Where C t = Aggregate Consumption Expenditure in Australia, quarterly data for the per
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Sheldon as the day for the challenge gets closer wants to enter the race. Not being content with an equal start, he wants to handicap himself by giving the other yachts a head star
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