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

Linear approximations, Linear Approximations In this section we will l...

Linear Approximations In this section we will look at an application not of derivatives but of the tangent line to a function. Certainly, to get the tangent line we do have to

Population problem - nonhomogeneous systems, The next kind of problem seems...

The next kind of problem seems as the population problem. Back in the first order modeling section we looked at several population problems. In such problems we noticed a single po

What is the smaller probable value of this number, The sum of the square of...

The sum of the square of a number and 12 times the number is -27. What is the smaller probable value of this number? Let x = the number.  The statement that is "The sum of the

Find the height of the lighthouse, Two  ships  are  sailing  in  the  sea  ...

Two  ships  are  sailing  in  the  sea  on  either  side  of  a  lighthouse;  the  angles  of depression of two ships as observed from the top of the lighthouse are 600  and 450 re

Estimate the cost of the car, Kyra receives a 5% commission on every car sh...

Kyra receives a 5% commission on every car she sells. She received a $1,325 commission on the last car she sold. What was the cost of the car? Use the proportion part/whole =

Project, report on shares and dovidend using newspaper

report on shares and dovidend using newspaper

Decision-making under conditions of uncertainty, Decision-Making Under Cond...

Decision-Making Under Conditions of Uncertainty With decision making under uncertainty, the decision maker is aware of different possible states of nature, but has insufficient

Simpson rule - approximating definite integrals, Simpson's Rule - Approxima...

Simpson's Rule - Approximating Definite Integrals This is the last method we're going to take a look at and in this case we will once again divide up the interval [a, b] int

30-60-90 degree triangle, : Find the length of the hypotenuse of a right tr...

: Find the length of the hypotenuse of a right triangle if the lengths of the other two sides are both 3 inches.

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