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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.
When Ms. Jones retired, she received a lump sum of $1,000,000 from her pension plan. She then invested this sum in an annuity account that would pay her an equal amount at the end
Kara borrowed $3,650 for one year at an annual interest rate of 16%. How much did Kara pay in interest? To ?nd out 16% of $3,650, multiply $3,650 through the decimal equivalent
how are indian customers visiting shoppers stop any different from customers of developed western countries
Probability -Probability is an extremely popular concept in business management. Since it covers the risks such may be included in certain business situations. This is a fact
Prisoners Dilemma This is a type of non-zero sum game and derives its name from the given story: The district attorney has two bank robbers in separate cells and offers them
use venn diagram to present
Function composition: The next topic that we have to discuss here is that of function composition. The composition of f(x) & g(x) is ( f o g ) ( x ) = f ( g ( x )) In other
just want to go over it
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Childrens errors are a natural and inevitable part of their process of learning. In the process of grasping new concepts, children apply their existing understanding, which may
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