Question

Consider the function f(x,y) = xy - 3x-2y2 + 17x + y + 37 and the constraint glx.v) = -6x + 3y - 12. Find the optimal point o
0 0
Add a comment Improve this question Transcribed image text
Answer #1

Here f(x,y) = xy-3x - 2y² + 17x + y + 37 Constraint glx,y) = -6x + 3y = 12 = guy) - 62 + 3y -12 We need to apply Lagranges Mab txry) = Аў8 Dry) ЧЕ () - (Бя, 4) Бx = у – 62 +1 Бу: 2 – Ҷу +1 9. – у = Substituting these values in Ф Үч-бап), чун 1) - A(compoully coefficient and d=2-44 tl y - 6x + 17 =-62 2-4y +1 = 31 > x=y-6x +17 -6 Comparing both > y-62 +17 - x-4y+ 3 - -6-218 - 11 4 40 у 2 2 2 Ч flacy) = -3 bc.y) = -3 1 3 4 22 toy) -20 22 3 Дcx,y) = -10422 #3 12 -3 Ч 9 b tx,y) = 48 -3 - Чs 1. 8s

Add a comment
Know the answer?
Add Answer to:
Consider the function f(x,y) = xy - 3x-2y2 + 17x + y + 37 and the...
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for? Ask your own homework help question. Our experts will answer your question WITHIN MINUTES for Free.
Similar Homework Help Questions
  • 12 pts Consider the function f(x,y) = xy - 3x - 2y + 17x+y+37 and the...

    12 pts Consider the function f(x,y) = xy - 3x - 2y + 17x+y+37 and the constraint olx.1) -- 6x + 3y = 12. Find the optimal point of f(x,y) subject to the constraint (.). Enter the values of r, y. f(x,y), and below. NOTE: Enter correct to 2 decimal places. y = f(x,y); =

  • Consider the function fix.) - xy - 3x - 2y + 17x+y+37 and the constraint x....

    Consider the function fix.) - xy - 3x - 2y + 17x+y+37 and the constraint x. - - 6x + 3y - 12. Find the optimal point of f(x,y) subject to the constraint oxy). Enter the values of, . fl.), and below. NOTE: Enter correct to 2 decimal places X=8.50 a у f(xy) - 6.50,3 A 3.83

  • Find the extreme values of the function f(x, y) = 3x + 6y subject to the...

    Find the extreme values of the function f(x, y) = 3x + 6y subject to the constraint g(x, y) = x2 + y2 - 5 = 0. (If an answer does not exist, maximum minimum + -/2 points RogaCalcET3 14.8.006. Find the minimum and maximum values of the function subject to the given constraint. (If an answer does not exist, enter DNE.) f(x, y) = 9x2 + 4y2, xy = 4 fmin = Fmax = +-12 points RogaCalcET3 14.8.010. Find...

  • Questions A and E (b) f(x, y) = 2.2-2y2-6x + 8y + 3 (c) f(z, y)=x2...

    Questions A and E (b) f(x, y) = 2.2-2y2-6x + 8y + 3 (c) f(z, y)=x2 + 6ry + 2/-6x +10y-2 Constrained Optimization 3. Find the values of r and y that maximize (or minimize) f(x,y) subject to the following constraints (a) f(z, y) = ry, subject to x + 2y = 2 (b) f(z, y)y+4), subject to z+y 8 (c) f(x,y) = x-3y-xy, subject to x + y = 6 (d) f(x, y)-7-y 2, subject to z ty 0...

  • pls solve like example Assign 7.3.25 Find all local extrema for the function f(x,y) = x3...

    pls solve like example Assign 7.3.25 Find all local extrema for the function f(x,y) = x3 - 12xy + y. Find the local maxima. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. There are local maxima located at (Type an ordered pair. Use a comma to separate answers as needed.) OB. There are no local maxima. Question Hel Find all local extrema for the function f(x,y)=x°-21xy+y3. The function will have local...

  • The function f(x,y)=3x + 3y has an absolute maximum value and absolute minimum value subject to...

    The function f(x,y)=3x + 3y has an absolute maximum value and absolute minimum value subject to the constraint 9x - 9xy +9y+= 25. Use Lagrange multipliers to find these values. The absolute maximum value is (Type an exact answer.) The absolute minimum value is . (Type an exact answer.)

  • In 11,) Find = classify any relative extrema Of f(x,y)=2x² 4 xy + 2 / 4...

    In 11,) Find = classify any relative extrema Of f(x,y)=2x² 4 xy + 2 / 4 g 12.) Use the method of Lagrange multipliers to minimize f(x, y) = x² + y² subject to the constraint equation - 3x + g = 30 (You do NOT have to verify that it is a minimum.

  • (a) If /(, y) = xy - 2y2 for all (x,y) € R², find (a,b) such...

    (a) If /(, y) = xy - 2y2 for all (x,y) € R², find (a,b) such that f(a,b) = (4.0) (Note: V/(,y) is also referred to as the gradient of f at (x,y). (b) Let f(x,y) = xy + y2 for (x,y) € RIn which direction(s) is the direction derivative off at (3.2) equal to zero? (c) If f(x,y) = 723 + y, find /.0.0).

  • Locate all relative minima, relative maxima, and saddle points, if any. f (x, y) = e-(x2+y2+16x)...

    Locate all relative minima, relative maxima, and saddle points, if any. f (x, y) = e-(x2+y2+16x) f at the point ( Use Lagrange multipliers to find the maximum and minimum values of f subject to the given constraint. Also, find the points at which these extreme values occur. f (x, y) = xy; 50x² + 2y2 = 400 Enter your answers for the points in order of increasing x-value. Maximum: at / 1) and ( Minimum: at ( and (

  • 15.8.15 Question Help The function f(x,y) = 4x2 + y2 has an absolute maximum value and...

    15.8.15 Question Help The function f(x,y) = 4x2 + y2 has an absolute maximum value and absolute minimum value subject to the constraint x² + 6y + y² = = 40. Use Lagrange multipliers to find these values. The absolute maximum is & 11 ULUIT.JU, JU UI 40 15.8.23 Question Help The function f(x,y,z) = 2x +z has an absolute maximum value and absolute minimum value subject to the constraint x2 + 2y2 + 2z2 = 9. Use Lagrange multipliers...

ADVERTISEMENT
Free Homework Help App
Download From Google Play
Scan Your Homework
to Get Instant Free Answers
Need Online Homework Help?
Ask a Question
Get Answers For Free
Most questions answered within 3 hours.
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT