Please answer very soon will give rating surely When a consumer has quantities, x1 and 2, of apples and oranges respectively, hisutility is given byu(x1, x2)2/31/3X1 X2Given that each apple costs pi dollars and each orange costs p2 dollars, use the methodof Lagrange multipliers to find the bundle of goods, (x1, x2), that will maximise hisutility given that he spends M dollars on apples and oranges.[You are not required to justify the use of the method of Lagrange multipliers here.]Also find his maximum utility, U(M), and verify that U'(M) is equal to the value ofthe Lagrange multiplier.

Concept: Lagrangian function : The initial problem is reformulated as a result of the link between…

When a consumer has quantities, ₁ and ₂, of apples and oranges respectively, his utility is given by u(x1, x₂) 2/3 1/3 = X1 X₂ . Given that each apple costs p₁ dollars and each orange costs p2 dollars, use the method of Lagrange multipliers to find the bundle of goods, (x₁, x2), that will maximise his utility given that he spends M dollars on apples and oranges. [You are not required to justify the use of the method of Lagrange multipliers here.] Also find his maximum utility, U(M), and verify that U'(M) is equal to the value of the Lagrange multiplier.

When a consumer has quantities, ₁ and ₂, of apples and oranges respectively, his utility is given by u(x1, x₂) 2/3 1/3 = X1 X₂ . Given that each apple costs p₁ dollars and each orange costs p2 dollars, use the method of Lagrange multipliers to find the bundle of goods, (x₁, x2), that will maximise his utility given that he spends M dollars on apples and oranges. [You are not required to justify the use of the method of Lagrange multipliers here.] Also find his maximum utility, U(M), and verify that U'(M) is equal to the value of the Lagrange multiplier.

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

See similar textbooks

Similar questions

Use Lagrange multipliers to find the point (a,b) on the graphof y = e4x, where the value ab is as small as possible.P =
the 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..
Use Lagrange multipliers to find the given extremum. Assume that x and y are positive.
Suppose that a temperature of a metal plate is given by T(x,y)=x2+2x+y2, for points (x,y) on the elliptic plate defined by 6x2+5y2≤60. Find the maximum and minimum temperatures on the plate. Use Lagrange Multipliers to determine the absolute extrema of f on the indicated constraint.
Of all the points on the graph of z = 10 - x^2 - y^2 that lie above the plane x + 2y + 3z = 0, what point is the farthest from the plane? (Do not use Langrange multipliers)
Find max and min using lagrange multipliers
Use the method of Lagrange Multipliers to find the maximum and minimumvaluesof x2+y2 subject to the constraint x4+ y4=2
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.
In an open-top drawer, the material cost of the two sides is $240 per m2. The material cost of the back is $500 per m2. The material cost of the front and the bottom are $1000 per m2 and $100 per m2 respectively. Use the method of Lagrange multipliers to find the dimensions of the most economical drawer having a volume of 0.08m3.
Use Lagrange multipliers to find three positive numbers whose sum is 18 and the sum of whose squares is as small as possible.
Use Lagrange multipliers to find three positive numbers whose sum is 230 and whose product is maximum.
Find the maximum value of the function z = 8x-2y with the restrictions as shown by the feasible region above