A manufacturer's total production of a new product isP(L, K) = 1500L2/3K1/3where 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 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 capital, K, by one unit.

Name: A manufacturer's total production of a new product isP(L, K) = 1500L2
Uploaded: 2024-03-20T07:07:26.000Z
Channel: Bartleby
Description: A manufacturer's total production of a new product isP(L, K) = 1500L2/3K1/3where 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 capita

Answered: Image /qna-images/answer/e9847853-d8bc-4012-80d8-0055d7d27475.jpg

Math

Advanced Math

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 c. $360,000. (a) To maximize production, how much should be spent on labor? 2$ How much on capital? $ (b) Find the value of the Lagrange multiplier. Give an interpretation of the Lagrange multiplier.

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 c. $360,000. (a) To maximize production, how much should be spent on labor? 2$ How much on capital? $ (b) Find the value of the Lagrange multiplier. Give an interpretation of the Lagrange multiplier.

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

See similar textbooks

Related questions

Q: A company produces two goods in quantities x and y, which it sells for the unit-prices $8 and $18…

A: To find the profit-maximizing level of y, we need to maximize the profit function. Profit (P) is…

Q: Consider the following model of a market for a good, in which Qs is quantity produced, Qd is…

A: The objective of the question is to find the value of Qs when Qs = Qd in the given market model.

Q: 12. Profit An apple orchard produces annual revenue of $50 per tree when planted with 1000 trees.…

A: The maximum of a function can be obtained by differentiating the function and equating it to 0. The…

Q: Consider the following model of a market for a good, in which Qs is quantity produced, Qd is…

A: The objective of this question is to find the price (P) when the quantity supplied (Qs) equals the…

Q: Suppose the production function for an airframe is Q = LK (Quantity = labor x capital) The price of…

Q: The table shows cost, C(q), and revenue, R(q). What are the fixed costs? 600 1200 1800 2400 3000…

A: Fixed cost is the cost is the initial cost of production i.e.., cost of production when no goods are…

Q: Amanufacturer of produces two types dowel and cross-country. The times required for manufacturing…

A: From the given data,Let number of downhill skis producednumber of cross-country skis…

Q: The cost that vary accordingly to the volume of output is _____________. a. All the options b.…

A: Given query: Need to find correct option about cost.

Q: If a small country with a demand of P= 80 - 2Q and a supply of P = 40 + 2Q decides to provide an…

A: We can rewrite the demand and supply equations in terms of P. So our demand equation becomes Q =…

Q: using the following: Input: Labor: $10000, material: $5200, overhcad: $20000. Keep in mind the Q2.B-…

Q: A 14-ton ship can carry four different types of cargo. The table below shows the weight in tons of…

A: A 14 ton ship carry four different types of cargo. The given details are, Types Load weight…

Q: Domino’s Pizza sells 300 Pizza in a day. The cost of raw materials per Pizza is 0.500, cost of…

Q: (b) The delivered cost of the concrete is "$150 per cubic yard (in increments of cubic yard) plus a…

A: Solution: Given that The delivered cost of concrete is $ 150 per cubic yard. $ 50 surcharge for…

Topic Video

Question

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 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 capital, K, by one unit.

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Step 3

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 3 steps with 3 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Optimization$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, advanced-math and related others by exploring similar questions and additional content below.

Similar questions

1
Suppose demand is given by p = 1600 − x. Find the maximum revenue.
Plz answer correctly asap
rials eo uations ow....zip Process . @ 2 D W Yaster Outfitters manufactures and sells extreme-cold sleeping bags. The table below shows the price-demand and total cost data, where: D • p is the wholesale price (in dollars) of a sleeping bag for a weekly demand of a sleeping bags; . C is the total cost (in dollars) of producing a sleeping bags. x (sleeping bags) p ($) 95 240 235 155 50 120 180 220 Use this data to create regression models to answer all of the questions below. #3 Price Model Find a quadratic regression equation for the price-demand data, using a as the independent variable. E p=a+bx+cr² Round a to the nearest integer, round b to 2 decimal places, and round c to 4 decimal places. Use this price model to answer question 1-2 below. $ 4 5 6 MacBook Pro C ($) 13,000 14,300 18,500 21,000 Y PEAR & * 8 ( 9 0 0 P A
The production function of a company is: q = 16 L+ 15 K - K?/5 - 2 L²/ 10 - 3 where "q" is the quantity of mobile phones produced per day, “L" is the number of employees, and "K" is the units of capital worth USD 10,000. The cost of unit capital per day is USD 20. and the average monthly salary of an employee is USD 1,200. The management wants you to find the optimal values of “q", “K" and “L" in order to maximize profit, if the unit selling price of each mobile phone is USD 100.
i. What is the total cost?
17 The demand D for a product at price x is given by D = + 20. Find (4 + 20) and state the result. dr