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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.
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
Tied Rankings A slight adjustment to the formula is made if several students tie and have the similar ranking the adjustment is: (t 3 - t)/12 Whereas t = number of tied
Q. How to Left shifts and right shifts a graph? Ans. When you're translating (shifting) a graph, it's easy to get subtracting and adding mixed up. It seems counter-intuiti
The vertices of a ? ABC are A(4, 6), B(1. 5) and C(7, 2). A line is drawn to intersect sides AB and AC at D and E respectively, such that AD/AB = AE/AC = 1/4 .Calculate the ar
I need help with my calculus work
Factoring By Grouping It is a method that isn't utilized all that frequently, but while it can be used it can be somewhat useful. Factoring by grouping can be nice, however it
Suppose you start saving today for a $55,000 down payment that you plan to make on a house in 7 years, assume that you make no deposits into the account after the initial deposit,
a boy is six months old his sister was given birth to three month after him. if their cousin is 0.33years old, arrange their ages in ascending order
Theorem Consider the subsequent IVP. y′ = p (t ) y = g (t ) y (t 0 )= y 0 If p(t) and g(t) are continuous functions upon an open interval a o , after that there i
Go back to the complex numbers code in Figures 50 and 51 of your notes. Add code fragments to handle the following: 1. A function for adding two complex numbers given in algeb
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