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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.
Aaron is installing a ceiling fan in his bedroom. Once the fan is in motion, he requires to know the area the fan will wrap. What formula will he use? The area of a circle is π
How to Solving One-Step Equations? Equations, where one math operation is acting on the variable, can be solved in one step. The trick is to get the variable x by itself - isol
Index Shift - Sequences and Series The main idea behind index shifts is to start a series at a dissimilar value for whatever the reason (and yes, there are legitimate reasons
Model of 180 meter tall building using a scale of 1.5 centimeters = 3.5 meters. How tall will the model be?
Find the area of shaded region, if the side of square is 28cm and radius of the sector is ½ the length of side of square.
2/4 + 3/4 =
can you help me with math
0+50x1-60-60x0+10
how to change order and variable in multiple integral
Q. How to Subtract fractions with different denominators? Ans. As with adding fractions, you can't subtract unless the denominators are the same. Here is an example: 9/
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