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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.
Question 1: What is the minimum number of students each of whom comes from one of the 50 different states, enrolled in a university to guarantee that there are at least 100 who
The angles between three non-zero and non coplanar vectors a,b and c are α between b and c and β between c and a and γ between a and b. The vector u and v are defined by u=(aX
2.46825141458*1456814314.446825558556
This time we are going to take a look at an application of second order differential equations. It's now time take a look at mechanical vibrations. In exactly we are going to look
please give the answer 1/9+1/3 with working out
How to raise Powers of Monomials ? To raise a monomial to a certain power: Step 1: Place the entire monomial inside parentheses, and place the desired power outside the paren
Green Bank charges a monthly fee of $3 for a checking account and $.10 per check. Savings-R-Us bank charges a $4.50 monthly fee and $.05 per check. How many checks required to be u
rouding each number to the nearest half
just want to go over it
The amount of particulate matter left in solution during a filtering process is given by the equation p(n) = 500(2) -0.8n , where n is the number of filtering steps. Find the amoun
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