Find the extremum of​ f(x,y) subject to the given​ constraint, and state whether it is a maximum or a minimum.   f(x,y)= 3x^2+4y^2 ; 2x+2y=28

Q: Find the minimum distance from the point (5, 0, 0) to the paraboloid z = x2 + y2. (Give your answer…

A: Given:    z = x2 + y2  Point: ( 5, 0, 0 )

Q: Find the maximum value of z = xy2 subject to 2x2 + y2 = 294; x ≥ 0, y ≥ 0. z =

A: Given information : z = xy2  subject to  2x2 + y2 = 294;  x≥0;  y≥0.

Q: 2. Find the critical points and determine whether they are a maximum, minimum or neither. y = a° –…

A: In the question we have to find the critical point also max. and min. points.

Q: Use the method of Lagrange multipliers to find the minimum distance from the origin (0, 0) to the…

A: We need to use the method of Lagrange's multiplier to determine the minimum distance from the point:…

Q: Find the extremum of f(x,y) subject to the given constraint, and state whether it is a maximum or a…

A:

Q: Find the extrema of f subject to the stated constraint f(x, y) = 3x + 2y, subject to 2x2 + 3y2…

A: Given:- f(x,y)=3x+2y ........................ (1)  and subject to 2x2+3y2=6…

Q: Find the minimum value of f(x, y, z) = x² + 2y² + 3z? subject to the constraint x + 2y + 3z = 10.…

A: Consider the given: fx,y,z=x2+2y2+3z2Subject to constraints:x+2y+3z=10gx,y,z=x+2y+3z−10 Use…

Q: 5. What is the maximum vertical distance between the line y = x + 2 and the parabola y = x² for – 1…

A: The given equations are, y = x + 2       ....(1)  y = x2            ....(2) To find the maximum…

Q: Find the minimum value of f (x, y) = xy subject to the constraint 5x - y = 4 in two ways: using…

A:

Q: Find the maximum value of f(x, y, z) = xy + xz+ yz – 4xyz subject to the constraints x + y + z = 4…

A: Given f(x, y, z) = xy + xz+yz - 4xyz subject to the constraints x + y + z = 4 and x, y, z ≥ 0 To…

Q: Find the minimum value of f(x, y, z) = 2x2 + y2 + 3z2 subject to the constraint 2x − 3y − 4z = 49.

A: Given: Function=f(x,y,z)= 2x2+y2+3z2 Constraint: 2x-3y-4z=49

Q: What is the maximum vertical distance between the line y = x + 51 and the parabola y= x² over the…

A: Given: The line y=x+51 and the parabola y=x2 To find: Maximum vertical distance between given line…

Q: Find constants a and b so that the minimum for the parabola f(x) = x- + ax + bis at the point (5,…

A:

Q: 3. For curve y ==x +4x2 - 12x , locate the possible maximum and minimum %3D points.

A:

Q: Find the least squares quadratic which best fits the curve Y= ex interval •< X<I ao+aix +azx over…

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Q: What is the maximum vertical distance between the line y = x + 2 and the parabola y = x2 for −1 ≤ x…

A: Consider the given line

Q: Find the extremum of f(x,y) subject to the given constraint, and state whether it is a maximum or a…

A: The subject to constraint can be used to find the value of y and then plugging it into the function…

Q: Find the minimum distance from the point (6, 0, 9) to the plane x – y + z = 5. (Hint: To simplify…

A:

Q: Find the two (x, y, z) points on the surface z² = x² + 3y² that are closest to the point (2, 2, 0)…

A: The surface is z2=x2+3y2. Obtain the distance of the point x, y, z to the point 2, 2, 0: Dx, y,…

Q: Calculate the point on the surface z =1 - x2 - y2 that has a maximum value for the sum of its…

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Q: Find the minimum distance from the parabola x – y = 0 to the point (0, 3). Minimum distance = %3!

A: At P(x,y), the point of shortest distance the slope of the line from P to (0,3) must be…

Q: Find the maximum of f (x, y, z) = xyz subject to the constraintg(x, y, z) = 2x + y + 4z = 1.

A: Let us assume  fx,y,z=xyz and gx,y,z≡2x+y+4z−1=0Using lagrange multiplier…

Q: Find the extremum of f(x,y) subject to the given constraint, and state whether it is a maximum or a…

A:

Q: What is the minimum vertical distance between the parabolas y = x² + x en y = x – x²?

A:

Q: Find maximum and minumum values of f(x, y, z) = 8x – 16y + 40z subject to the constraint x? +y² + z²…

A:

Q: Find the extremum of f(x.y) subject to the given constraint, and state whether it is a maximum or a…

A: Legranges multiplier

Q: Find the minimum distance from the point (6, 0, 9) to the plane x - y + z = 5. (Hint: To simplify…

A: Given plane is x-y+z=5 and the point is (6,0,9) normal to the plane is (1,-1,1)

Q: 1. Find the maximum value of f(x, y) = 4xy where x > 0 and y > 0, subject to the constraint 9. = 1.

A:

Q: Find the minimum distance from the point (6, 1, 6) to the plane x - y + z = 6. (Hint: To simplify…

A: To find the minimum distance from the point (6,1,6) to plane x - y + z = 6. By using formula,…

Q: Find the minimum distance from the cone z = 2x2 + y2 to the point (-6, 4, 0).

A: To find the minimum distance first write distance function. Which is the square distance from  .

Q: Find the maximum and minimum values of the function f(x, y, z) = 3x – y – 3z subject to the…

A:

Q: Find the minimum distance from the parabola x − y2 = 0 to the point (0,3) Minimum distance =

A:

Q: Find the maximum and minimum values of the function f(x, y, z) = 3x - y - 3z subject to the…

A:

Q: Find the maximum of f(x, y, z) = x + y + z subject to the two constraints x2 + y² + z² = 4 and x² +…

A: Step:-1 Given that f(x,y,z)=x+y+z subject to  x2+y2+z2=4⇒x2+y2+z2-4=0…

Q: By minimizing the function ƒ(x, y, u, y) = (x - u)2 + (y - y)2 subject to the constraints y = x + 1…

A:

Q: what is the minimum vertical distance between parabolas y = x2 + 4 and y = x -x2

A: Given: The equations of two parabolas are: y1=x2+4 y2=x-x2 We have to find the minimum vertical…

Q: What is the maximum vertical distance between the y=x+2 and the parabola y=x^2 for -1 is less than…

A:

Q: Find the minimum distance from the point (2, 1, 9) to the surface x + y + z = 9.

A:

Q: Find the minimum distance from the cone z = √(x2 + y2) to the point (-6, 4, 0).

A: To find the minimum distance

Q: simplex method

A: We have to solve the given problem by simplex method.

Q: Find the point where the function f(x,y,z) = x + 2y + 3z subject to the constraint xyz= 2 takes on…

A: Answer is in below steps.

Q: Find the maximum value of f(x, y) = 4xy(9 – 72x – 9y) over the triangle with vertices -- - (0,0), (5…

A: Given: fx,y=4xy9-72x-9y vertices 0,0 18,00,1

Q: Determine the minimum distance from the point (5, –1) to the parabola given byy = x², using Lagrange…

A: To find the minimum distance first form the function using the square of the distance formula…

Q: Find the maximum and minimum values of f (x, y, z) = xyz subject to the constraint x2 + 2y2 + 4z2 =…

A: Our guidelines for multiple questions, answer only first question  For 2 answer , repost the…

Q: Find the minimum of the function f(x, y) = 2x² + 2y² subject to the constraint z + y – 1= 0. Value…

A: Here we have to solve the above problem by using Lagranges's multiplier and then differentiate and…

Q: Find the minimum distance from the cone z= to the point (6, 6, 0).

A:

Q: Find the extremum of​ f(x,y) subject to the given​ constraint, and state whether it is a maximum or…

A: Solution:-  the given constraints are  f(x,y) = xy and 14x+y=8 we have to find extremum....

Maximization

Have you ever seen a bridge in the shape of a parabola? Where is its maximum on the bridge? The maximum of that bridge is the highest point on that bridge. The process of finding the maximum of the bridge here is called the maximization.