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: 2 = 40p.5 p0.5 Chemical P costs $200 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 $32,000. 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
Solve using Lagrange multipliers. (The stated extreme values do exist.) A company manufactures two products, in quantities x and y. Because of limited materials and capital, the quantities produced must satisfy the equation 2x2 + 5y2 = 46,800. (This curve is called a production possibilities curve.) y 120 2x +5 y = 46,800 100 80 60 40 20 50 100 150 (a) If the company's profit function is P = 4x + 5y dollars, how many of each product should be made to maximize profit? y = (b) Find the maximum profit (in dollars).
3. Solve by Lagrange Multiplier Method: Clearly identify your constraint function and your system. You may use either approach you learned in class and on the video. The annual production of skateboards at a local factory is described by the equation: U (x,y) = 800x(1/4) y(3/4) where x is worker-hours and y is capital expenditure (measured in units of $10 dollars). Manufacturing costs the factory roughly 10x + 20y dollars. a) What values of x and y will allow the factory to maximize the production of skateboards while spending only $600?
Minimise x2+y−2xyx2+y−2xy subject to the constraint y=1
(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 chemical manufacturing plant can produce z units of chemical Z given p units of chemical P and r units of chemical R, where: z = 100p-75,0.25 Chemical P costs $100 a unit and chemical R costs $700 a unit. The company wants to produce as many units of chemical Z as possible with a total budget of $112,000. 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

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