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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.
what is the quotient of 20x to the power of 2 y-16x y to the power of 2+ 8xy and -8xy
-7-5
If the expression 9y - 5 represents a certain number, which of the following could NOT be the translation? a. five less than nine times y b. five less than the sum of 9 and y c
If three times the larger of the two numbers is divided by the smaller, then the quotient is 4 and remainder is 5. If 6 times the smaller is divided by the larger, the quotient is
If the following terms form a AP. Find the common difference & write the next 3 terms3, 3+ √2, 3+2√2, 3+3√2.......... Ans: d= √2 next three terms 3 + 4 √ 2 , 3 + 5√ 2 ,
what is the difference between North America''s part of the total population and Africa''s part
Assume company A expects to enhance unit sales of i-phone by 15% per year for the next 5 years. If you presently sell 3 million i-phones in one year, how many phones do you expect
Example Show that p ( x ) = 2 x 3 - 5x 2 -10 x + 5 has a root somewhere in the interval [-1,2]. Solution What we're actually asking here is whether or not the function wi
Simplify following and write the answers with only positive exponents. (a) ( x 8.2 y -0.26 z 2 ) 0.5 (b) (x 3 y -4.1 / x -2.7 ) -3 Solution (a) (x 8.2
Find the second derivative of the below given equation Y= e x cosx
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