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Erercise 6.3.3. Using the Lagrange multiplier method, solve each of the following con- strained optimization problems:81Maximize f(x,y) 10zy if 3x + Sy = 45.(b) Min...

Question

Erercise 6.3.3. Using the Lagrange multiplier method, solve each of the following con- strained optimization problems:81Maximize f(x,y) 10zy if 3x + Sy = 45.(b) Minimize f(x,y) = 30zy I2 _ 4y? if Ty 200.

Erercise 6.3.3. Using the Lagrange multiplier method, solve each of the following con- strained optimization problems: 81 Maximize f(x,y) 10zy if 3x + Sy = 45. (b) Minimize f(x,y) = 30zy I2 _ 4y? if Ty 200.



Answers

Use Lagrange multipliers to find the given extremum. In each case, assume that $x, y,$ and $z$ are positive. $$ \begin{array}{l}{\text { Minimize } f(x, y)=x^{2}-8 x+y^{2}-12 y+48} \\ {\text { Constraint: } x+y=8}\end{array} $$

Later on Today we're going to solve a problem. Number eight here we have to maximize function of expires that equals eight square by square, that square subject toe X square plus white square. Plus that square minus one equals zero. We have f with respect to taxes. Two weeks. Why square that square minus too long Nights equals zero. If with respect to boys to my ex square that square minus to land away equals zero If with respect to their dick was does it x square by square minus to love doesn't equals zero If with respect to long like was X squared plus y squared Plus that square minus learn it was zero So why square that square? Because X square by square recalls what a square they're square equals X square by square equals X square by square So it's a square plus why square president square equals smart which has a solution off one bedroom three Come on, one There are three comma, one by route. Thank you

Everyone trigger going to solve program number 15, they have to minimize function of with Jessica's Ex Square that's like Square Pleasure Square, subject to X plus y Pleasant minus one equals zero. They had to define F ex like lambda equals X squared plus y squared plus that square minus lambda in the X Plus y. Plus that minus smart, if with respect, Lexus two. X Men is Lambda equals zero if with respect to ways to my mind slammed up because zero, if with respect to that is two's admirers, Lambda equals zero. If with respect to Lambda because X plus y plus that minus Monaco's zero real executes vehicles that and X plus y plus that minus one equals zero. So X comma comma is that it was one by three comma one by three comma one by three Thank you

101 Canadian going to sort problem Number 17. Here we are to maximize function of what do you think? It's common way. Jessica's Eggs sequence by plaza subject to Constraints X Square plus my square Pleasure Square minus one equals zero. We had to define as at ex My laptop sequence X plus y plus X minus lambda in do X squared. That's why it's square. Does that square my smart f with respect to access one minus to London, Mexico zero have with respect of I is one minus to land a very cool zero f with respect to other days. One minus two Long does that Because zero if with respect to Lambda, because exit square breast lightsquared First that square minus Monica was zero. Well executes vehicles that and X square plus white square Blizzard square minus one equals zero. I didn't have the solution at one Beirut. Three. Like the Route three and one Beirut. Three. Thank you

Hello, everyone. Today we are going to fall. Problem number 14 Here we had to maximize function of X com over equals Excellent that subject Toe express White prosthetic minus six Because zero we have to defend F at X y lambda because exquisite minus lambda in tow, X plus y pleasant minus six equals zero. If with respect to access why is that mine? Islam, like zero with respect over is it said mine. Islam d equals zero. If with respect user this x Y minus lambda If with respect to long guys X plus y Pleasant minus six equals zero build X equals y equals that X plus y pleasant minus six Because zero which is a solution X y is that it was two comma, two commas took Thank you.


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