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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.
A number of the form x + iy, where x and y are real and natural numbers and is called as a complex number. It is normally given by z. i.e. z = x + iy, x is called as the real part
In this part we look at another method to obtain the factors of an expression. In the above you have seen that x 2 - 4x + 4 = (x - 2) 2 or (x - 2)(x - 2). If yo
Now we start solving constant linear, coefficient and second order differential and homogeneous equations. Thus, let's recap how we do this from the previous section. We start alon
i can not figer out my homework it says "USE THE MAKE AN ORGANIZED LIST STRATEGY,Medeline bikes 4 laps around her neighborhood 2 times a week.How many laps does she bike in 8 weeks
Graph y = sin ( x ) Solution : As along the first problem in this section there actually isn't a lot to do other than graph it. Following is the graph. From this grap
how will the decimal point move when 245.398 is multiplied by 10
Verify Liouville''''''''s formula for y "-y" - y'''''''' + y = 0 in (0, 1) ?
11/20=
A man invests rs.10400 in 6%shares at rs.104 and rs.11440 in 10.4% shares at rs.143.How much income would he get in all??
Jackie invested money in two different accounts, one of that earned 12% interest per year and another that earned 15% interest per year. The amount invested at 15% was 100 more tha
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