4.DETAILSSCALCET8M 14.8.009.MY NOTESASK YOUR TEACHERPRACTICE ANOTHERThis extreme value problem has a solution with both a maximum value and a minimum value. Use Lagrange multipliers to find the extreme values of the function subject to the givenconstraint.f(x, y, z) = xy2z; x2 = y2 + z2 = 36maximum value6.minimum value-6Additional MaterialsD eBookViewing Seved Work Revert to Last Response

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Algebra for College Students

10th Edition

ISBN:9781285195780

Author:Jerome E. Kaufmann, Karen L. Schwitters

Publisher:Jerome E. Kaufmann, Karen L. Schwitters

Chapter12: Algebra Of Matrices

Section12.CR: Review Problem Set

Problem 35CR: Maximize the function fx,y=7x+5y in the region determined by the constraints of Problem 34.

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A function, z = ax + by, is to be optimized subject to the constraint, x2 + y2=1 where a and b are positive constants. Use Lagrange multipliers to show that this problem has only one solution in the positive quadrant (i.e. in the region x > 0, y > 0) and that the optimal value of z is √a2 +b2.
Consider the following optimisation problemmin f(x, y) = x + y − x2subject to x + y ≤ 1x ≥ 0, y ≥ 0.a) Find a critical point of the Lagrangian.b) Find a better solution to the problem above than the critical point ofthe Lagrangian calculated in a).c) What sufficient condition for the optimality of the Lagrangian solutionis violated by the problem.
13.6_4 Can you please help with a step by step guide? Thank you very much in advance. Use Lagrange multipliers to find the given extremum. Assume that x and y are positive. Minimize f(x, y) = 2x + y Constraint: xy = 18 Minimum of f(x, y) = ? AT (x, y) = ?
Although ∇ƒ = l∇g is a necessary condition for the occurrence of an ex-treme value of ƒ(x, y) subject to the conditions g(x, y) = 0 and ∇g ≠ 0, it does not in itself guarantee that one exists. As a case in point, try using the method of Lagrange multipliers to find a maximum value of ƒ(x, y) = x + y subject to the constraint that xy = 16. The method will identify the two points (4, 4) and (-4, -4) as candidates for the location of extreme values. Yet the sum x + y has no maximum value on the hyperbola xy = 16. The farther you go from the origin on this hyperbola in the first quadrant, the larger the sum ƒ(x, y) = x + y becomes.
Suppose f(x,y)=x2+y2−2x−2y+1f(x,y)=x2+y2−2x−2y+1 (A) How many critical points does ff have in R2R2? (B) If there is a local minimum, what is the value of the discriminant D at that point? If there is none, type N. (C) If there is a local maximum, what is the value of the discriminant D at that point? If there is none, type N. (D) If there is a saddle point, what is the value of the discriminant D at that point? If there is none, type N. (E) What is the maximum value of ff on R2R2? If there is none, type N. (F) What is the minimum value of ff on R2R2? If there is none, type N.
At noon, ship A is 45 miles south of Ship B. Ship A is sailing north at a rate of 15 miles per hour. Ship B is sailing west at a rate of 15 miles per hour. When is the distance between the two ships minimized? In the field below enter the time at which the distance between the ships is minimal.

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This extreme value problem has a solution with both a maximum value and a minimum value. Use Lagrange multipliers to find the extreme values of the function subject to the given constraint. r(x, y, z) = xy2z; x²+ yZ + z? = 36