Find out the minimum distance from the origin, Mathematics

Assignment Help:

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.

 


Related Discussions:- Find out the minimum distance from the origin

Maximum and minimum values, Find all the local maximum and minimum values a...

Find all the local maximum and minimum values and saddle points of the function f(x, y) = x 2 - xy + y 2 + 9x - 6y + 10

Substitution rule, Substitution Rule ∫ f ( g ( x )) g′ ( x ) dx = ∫ f (...

Substitution Rule ∫ f ( g ( x )) g′ ( x ) dx = ∫ f (u ) du,     where, u = g ( x ) we can't do the following integrals through general rule. This looks considerably

Properties of summation notation, Properties Now there are a couple of ...

Properties Now there are a couple of formulas for summation notation. 1. here c is any number. Therefore, we can factor constants out of a summation. 2. T

Algebra2;, log6 X + log6 (x-5) = 1

log6 X + log6 (x-5) = 1

I NEED HELP, Teng is designing a house and in each room he can choose from ...

Teng is designing a house and in each room he can choose from tiles, floorboards, or carpet for the floor. a. How many combinations of flooring materials are possible if he designs

Decimal representations of some basic angles, Decimal representations of so...

Decimal representations of some basic angles: As a last quick topic let's note that it will, on occasion, be useful to remember the decimal representations of some basic angles. S

Linear equation, The sum of the digit number is 7. If the digits are revers...

The sum of the digit number is 7. If the digits are reversed , the number formed is less than the original number. find the number

Solve 6 sin ( x/2)= 1 on [-20, Solve 6 sin ( x/2)= 1 on [-20,30] Soluti...

Solve 6 sin ( x/2)= 1 on [-20,30] Solution Let's first work out calculator of the way since that isn't where the difference comes into play. sin( x/2)= 1/6   ⇒x/2= sin

Trig, I need help with this question: Find the probability that two quarter...

I need help with this question: Find the probability that two quarters and a nickel are chosen without replacement from a bag of 8 quarters and 12 nickles.

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd