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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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what does 1000/q in the ATC equation represent economically?
Integral Test- Harmonic Series In harmonic series discussion we said that the harmonic series was a divergent series. It is now time to demonstrate that statement. This pr
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DEVELOPING AN UNDERSTANDING : The other day I was showing the children's book '203 Cats' to my 7-year-old niece. She had recently learnt how to write large numerals in her school
(a) Using interpolation, give a polynomial f ∈ F 11 [x] of degree at most 3 satisfying f(0) = 2; f(2) = 3; f(3) = 1; f(7) = 6 (b) What are all the polynomials in F 11 [x] which
the wholesale p of string beans in dollars per bushel and the daily supply x in thousands of bushel,are related by the equation px+6x+7p=5950. if the supply is decreasing at the r
Find the second derivative of the below given equation Y= e x cosx
a
Determine if the line that passes through the points ( -2, -10) and (6, -1) is parallel, perpendicular or neither to the line specified by 7 y - 9 x = 15 . Solution Togive
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