find the local maxima of the function f(x,y) = 1 + x^2 + y^2 - 4xy with a constraint g(x,y) = x^2 + y^3 - 2 = 0?
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Q: Question 1 a. Use the method of Lagrange multipliers to find the extreme value(s) of f(x, y) = x² +…
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Q: 1) Suppose you want to optimize the function V = (x - 1)2 + (y + 1)2 + (z-1)2, hold it restriction…
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Q: The maximum value of f(x,y) = x +y subject to xy = 16 (using method of Lagrange multipliers) is 16
A: Given function is f(x,y)=x+y Constraint: xy=16
Hello,
I asked a similar question and the answer was quite helpful, but I have a followup.
How do I find the
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- Maximize the function fx,y=7x+5y in the region determined by the constraints of Problem 34.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.Find the point on the surface 4x+y-1=0 closest to the point (1,2,-3) using Larange Multipliers. I have only managed to determine that z=-3, but all the other x and y values I have solved for have not looked right compared to a graph.
- Discuss the advantages and disadvantages of the method of Lagrange multipliers compared with solving the equation g(x,y) =0 for y (or x), substituting that expression into f and then minimizing or maximizing f as a function of one variable.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.A firm has two plants, X and Y. Suppose that the cost of producing x units at plant X is x^2 + 12000 dollars and the cost of producing y units of the same product at plant Y is given by 3y^2 + 800 dollars. If the firm has an order for 1200 units, how many should it produce at each plant to fill this order and minimize the cost of production (use Lagrange multiplier)? Answer in complete solutions please. Thank you.
- Please reply as soon is posible, thanks! 1) Suppose you want to optimize the function V = (x - 1)2 + (y + 1)2 + (z-1)2, hold it restriction 4x + 3y + z = 2, using the Lagrange multipliers technique. If λ corresponds to the multiplier used when defining the Lagrange function, then one of the equations of the system to be solvedcorresponds to:A) 2 (y + 1) = λB) z - 1 - λ = 0C) 4x + 3y + z - 2 = 0D) 2 (x - 1) = 3λ 2) Suppose z is given implicitly by the equation x3y − yz2 +z/x = 4in a neighborhood of the point P (1, −2), in which z = −2. The value of the directional derivative of z at P in the direction of the vector w = (−3, −4), corresponds to:A) −24/7B) 24/35C) 24/7D) −24/35 3) Consider the solid Q bounded by the surfacesS1: x = 4 - z2S2: x + y = 5S3: x = 0S4: y = 0S5: z = 0shown in the figure. (See the Solid Q in the images) When projecting Q onto the Y Z plane, two subregions are determined. One such subregion is composed of the points (y, z) such that:A) 1 ≤ y ≤ 5, 0 ≤ z ≤ 1 + z2…Can I get some assistance with this coordinatization problem?Use two-phase simplex Method to solve the following LP Minimize z= 6 x1 + 3 x2 Subject to x1+x2 ≥ 1 2x1- x2 ≥ 1 3x2 ≤ 2 x1,x2 ≥ 0
- Can I get some help with this Coordinatization problem?Find the Max and Mini values of the objective function Z=3x+4y on the region bounded by 2x+y>5 x+5y>16 2x+y<14 -x+4y<20 Needs to be solved with the simplex methodthe quantity, q, of a product manufactures depends on the number of workers.W , and the amount of capital invested, K, and is represented by the Cobb-Douglasfunctionq = 64W^3/4 K^1/4 .Suppose further that labor costs $18 per worker and capital costs $28 per unit, and thebudget is $4600. Let λ be the Lagrange multiplier. Does increasing the budget by $1 allow theproduction of λ extra units of the product? Explain why as shown in the image below..