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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.
Simplify following and write the answers with only positive exponents. (-10 z 2 y -4 ) 2 ( z 3 y ) -5 Solution (-10 z 2 y -4 ) 2 ( z 3 y ) -5
A painting was purchased 11 years ago for $26900. It has just been sold for $78000. Calculate the flat rate of appreciation p.a.
cramers rule introduction
#question.Find the slope of the line that passes through (7, 3) and (9, 6). Simplify your answer and write it as a proper fraction, improper fraction, or integer. .
It's easier to describe an explicit solution, in this case and then tell you what an implicit solution is not, and after that provide you an illustration to demonstrate you the dif
If roots of (x-p)(x-q) = c are a and b what will be the roots of (x-a)(x-b) = -c please explain. Solution) (x-p)(x-q)=c x2-(p+q)x-c=0 hence, a+b=p+q and a.b=pq-c
For inequalities we contain a similar notation. Based on the complexity of the inequality the solution set might be a single number or it might be a range of numbers. If it is jus
Distance Traveled by Car - word problem: It takes a man 4 hours to reach a destination 1325 miles from his home. He drives to the airport at an average speed of 50 miles per h
HOW TO ADD MIXED FRACTION
Find the generating function for the number of r-combinations of {3.a, 5.b, 2.c} Ans: Terms sequence is given as r-combinations of {3.a, 5.b, 2.c}. This can be writte
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