A firm producing 2 goods, x and y, faces the cost function:C = 4x² + 5xy + 10y² + 50By using the Lagrangian method, find the cost minimising outputs if the firm also faces the production quota x + y = 120 as an additional constraint. What is the cost minimising output of good y?30352520None of the aboveO No answer

A firm producing 2 goods, x and y, faces the cost function:C=4x2+5xy+10y2+50By using the Lagrangian…

Answered: A firm producing 2 goods, x and y,…

Algebra and Trigonometry (6th Edition)

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

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A chemical manufacturing plant can produce z units of chemical Z given p units of chemical P and r units of chemical R, where: Chemical P costs $100 a unit and chemical R costs $400 a unit. The company wants to produce as many units of chemical Z as possible with a total budget of $80,000. 2= 100p0.8.0.2 A) How many units each chemical (P and R) should be "purchased" to maximize production of chemical Z subject to the budgetary constraint? Units of chemical P, p = Units of chemical R, r = B) What is the maximum number of units of chemical Z under the given budgetary conditions? (Round your answer to the nearest whole unit.) Max production, z= units
Minimise x2+y−2xyx2+y−2xy subject to the constraint y=1
A manufacturer's total production of a new product is P(L, K) = 1800L2/3K1/3 where L is the number of units of labor and K is the number of units of capital. A unit of labor costs $200, a unit of capital $800, and the total budget for labor and capital is $960,000. (a) To maximize production, how much should be spent on labor? 2$ How much on capital? 24 (b) Find the value of the Lagrange multiplier. Give an interpretation of the Lagrange multiplier. O The Lagrange multiplier is the approximate increase in the optimal value of P resulting from an increase in labor, L, by one unit. O The Lagrange multiplier is the approximate increase in the total budget for labor and capital resulting from an increase in the optimal value of P by one unit. O The Lagrange multiplier is the approximate increase in the optimal value of P resulting from an increase in the total budget for labor and capital by one unit. O The Lagrange multiplier is the approximate increase in the optimal value of P resulting…
The monthly income associated with the sale of two products is described with the function in two variables / = 21a + 19b, where a and b are quantities sold of products A and B, respectively. Furthermore, it is known that the cost of producing these products is modeled by C = 3a² +6b². With this information answer: Write the criterion of the monthly profit function from the sales of products A and B, use as variables a and b What is the only critical point of the utility function? What is the value of the discriminant of the utility function evaluated at that critical point (Value of D used to classify the critical point) At this critical point. Is a relative maximum, a relative minimum, or neither determined?
(2-T) ABC is a small manufacturer of two types of popular all-terrain snow skis, the J and the D models. The manufacturing process consists of two principal departments: fabrication and finishing. The fabrication department has 12 skilled workers, each of whom works 7 hours per day. The finishing department has 3 workers, who also work a 7-hour shift. Each pair of J skis require 3.5 labor hours in the fabricating department and 1 labor hour in finishing. The D model requires 4 labor hours in fabricating and 1.5 labor hours in finishing. The company operates 5 days a week. ABC makes a net profit of $50 on the J model and $65 on the D model. In anticipation of the next ski-sale season, ABC must plan its production of these two models. Because of the popularity of its products and limited production capacity, its products are in high demand, and ABC can sell all it can produce each season. The company anticipates selling at least twice as many D as J models. (Use Geogebra) Write your LP…
A manufacturer's total production of a new product is P(L, K) = 1500L2/3K1/3 where L is the number of units of labor and K is the number of units of capital. A unit of labor costs $100, a unit of capital $400, and the total budget for labor and capital is $360,000. (a) To maximize production, how much should be spent on labor? 2$ How much on capital? $ (b) Find the value of the Lagrange multiplier. Give an interpretation of the Lagrange multiplier. O The Lagrange multiplier is the approximate increase in the optimal value of P resulting from an increase in labor, L, by one unit. O The Lagrange multiplier is the approximate increase in the total budget for labor and capital resulting from an increase in the optimal value of P by one unit. The Lagrange multiplier is the approximate increase in the optimal value of P resulting from an increase in the total budget for labor and capital by one unit. O The Lagrange multiplier is the approximate increase in capital, K, resulting from an…
Solve the following optimization model using Excel Solver. Upload the final excel file. min 2x² + 5xz+8zy² s.t. 8x + 16y +21z ≥ 400 3x + 5y + 8z ≥ 160 4z² + 5xy ≤ 600 x,y,z≥0
A. Methods of finding characteristics roots of the quadratic equations. B. Maximize the utility function: U= Y1 + Y2 Subject to I = P1 Y1 + P2 Y2 Also find out demand functions
A firm has the following production function:q = ƒ (z1, z2) = z1αz2βb. Solve for the firm's conditional demand function (simplify)
2. In each of the following cases, write down the northwest corner rule solution and use the stepping stone method to find the minimal transportation cost. Supply 20 30 70 Source A B C Demand D 8 6 10 90 Destinations E 6 3 7 20 F 9 8 9 10

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