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

Arc length with parametric equations, Arc Length with Parametric Equations ...

Arc Length with Parametric Equations In the earlier sections we have looked at a couple of Calculus I topics in terms of parametric equations.  We now require to look at a para

Can religious wars be avoided in the future, To what extent do you think re...

To what extent do you think religious beliefs should justify war? How is this shown in "The Song of Roland"? Cite examples of how religious beliefs have led to war in the last two

Permuation and combination, how many words can be formed from letters of wo...

how many words can be formed from letters of word daughter such that each word contain 2vowles and 3consonant

Estimation of difference among two means-illustration, A comparison of the ...

A comparison of the wearing out quality of two types of tyres was obtained by road testing. Samples of 100 tyres were collected. The miles traveled until wear out were recorded and

Compute the value of the following limit, Compute the value of the followin...

Compute the value of the following limit. Solution: Notice as well that I did say estimate the value of the limit.  Again, we will not directly compute limits in this sec

Draw a common graph f ( x ) = - x2 + 2x + 3 , Graph        f ( x ) = - x 2 ...

Graph        f ( x ) = - x 2 + 2x + 3 . Solution It is a parabola in the general form.                              f ( x ) = ax 2 + bx + c In this form, the x-coor

Calculus online, need help completing my online text. can provide login det...

need help completing my online text. can provide login details

What is her weekly paycheck assuming there are deductions, Kyra's weekly wa...

Kyra's weekly wages are $895. A Social Security tax of 7.51% and a State Disability Insurance of 1.2% are taken out of her wages. What is her weekly paycheck, assuming there are no

Higher-order derivatives, Higher-Order Derivatives It can be se...

Higher-Order Derivatives It can be seen that the derivative of a function is also a function. Considering f'x as a function of x, we can take the derivative

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