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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.
Before taking up division of polynomials, let us acquaint ourselves with some basics. Suppose we are asked to divide 16 by 2. We know that on dividing 16 by
Explain Fermats Last Theorem? How to solve problems under Fermats Last Theorem?
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The area of a rectangle is 24 square inches. The length of the rectangle is 2 inches more than the width. How many inches is the width? Let x = the number of inches in the widt
A group of ?ve friends gone out to lunch. The total bill for the lunch was $53.75. Their meals all cost about the similar, so they needed to split the bill evenly. Without consider
how do i compute an algebra number
The Fisher's index The index of Fisher acts as a compromise between Paasche' index and Laspeyre's index. This is calculated as a geometric mean of the two indexes.
If n is positive integer greater than 1 and a & b both are positive real numbers then, Consider that on occasion we can let a or b to be negative and yet have these propert
korda ab e ndan rrethin me qender o ne dy harqe njeri prej tyre eshte sa trefishi i tjetrit gjeni masat e harqeve dhe masat e trekendeshit aob
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