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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.
Example of Log Rules: Y = ½ gt 2 where g = 32 Solution: y = 16 t 2 Find y for t = 10 using logs. log y = log 10 (16 t 2 ) log 10 y = log 10 16 + log 10
Mr.Tanaka has 56 students in his choir the ratio of boys to girls is 3:4 how many boys and girls are in his class
hi i am doing the oaks test do you have somthing that could help me
As1212uestion #Minimum 100 words accepted#
Can you help me find out how to find the surface area of a prism
Marketing management,Analysis,planning and implementation
A department store faces a decision for a seasonal product for which demand can be high, medium or low. The purchaser can order 1, 2 or 3 lots of this product before the season beg
A 4-inch by 6-inch photograph is going to be enlarged through increasing each side by the similar amount. The new area is 168 square inches. How many inches is each dimension incre
What is the determinant of a square matrix?
Evaluate the given limit. Solution : It is a combination of many of the functions listed above and none of the limited are violated so all we have to do is plug in x = 3
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