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

The stoichiometric reaction, Prove that a reaction following the rate law v...

Prove that a reaction following the rate law v = k[A] 2 is characterized by a linear plot of [P] t 1 versus t-l, where P is the product of the stoichiometric reaction A = P. Sho

Confidence interval, Confidence Interval The interval estimate or a 'co...

Confidence Interval The interval estimate or a 'confidence interval' consists of a range as an upper confidence limit and lower confidence limit whether we are confident that a

Find the least number that is divisible by all numbers, Find the  leas...

Find the  least  number that  is  divisible by all  numbers between 1  and  10  (both inclusive). Ans: The required number is the LCM of 1,2,3,4,5,6,7,8,9,10 ∴ LCM = 2  × 2

Calculate the amplitude of trigonometry function, Consider the trigonometri...

Consider the trigonometric function f(t) = -3 + 4 cos(Π/ 3 (t - 3/2 )). (a) What is the amplitude of f (t)? (b) What is the period of f(t)? (c) What are the maximum and mi

Matrices, Consider the following linear equations. x1-3x2+x3+x4-x5=8 -2x1+...

Consider the following linear equations. x1-3x2+x3+x4-x5=8 -2x1+6x2+x3-2x4-4x5=-1 3x1-9x2+8x3+4x4-13x5=49

Assumptions of interpolation and extrapolation, Assumptions The f...

Assumptions The figures known are assumed to be a normal series, that is a series without any violent, unexplained fluctuations in the values. The

Differential equation, Find the normalized differential equation which has ...

Find the normalized differential equation which has {x, xex} as its fundamental set

What is converse- inverse and contrapositive, What is Converse, Inverse, an...

What is Converse, Inverse, and Contrapositive In geometry, many declarations are written in conditional form "If ...., then....." For Example: "If two angles are right angles,

Define tautology and contradiction, Define tautology and contradiction.  ...

Define tautology and contradiction.  Ans: If a compound proposition comprises two atomic propositions as components, after that the truth table for the compound proposition con

Standardizing a random variable, Standardizing a Random Variable       ...

Standardizing a Random Variable       If X is a random variable with E(X) = m and V(X) = s 2 , then Y = (X – m)/ s is a random variable with mean 0 and standard deviatio

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