A manufacturer produces two types of products (x and y) and must decide howmany it should produce to sell in two different market segments. Suppose its profit func-tion (in hundred pesos) is defined by P(x, y) = 20x + 40y – 0.5x² – y² and the total outputis equal to 25. Use the method of Lagrange multipliers to find the values of x and y thatmaximizes profit and then find the maximum profit.

Answered: Image /qna-images/answer/026b9f9f-5617-4ee0-8db2-03bd7c55e6a3.jpg

Answered: A manufacturer produces two types of…

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 37CR

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Similar questions

Maximize the function fx,y=7x+5y in the region determined by the constraints of Problem 34.
Solve max f( x,y , z) 3x2+y problem by means of Lagrange multipliers under the constraints of 4x-3y=9 and x2+z2=9. Explain what the values of Lagrange multipliers mean?
Suppose that we want to optimize the function V = x2 + y2 + z3, subject to the restriction xyz = 4, 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 solved corresponds to:
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.
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..
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.

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