Let Srepresent the amount of steel produced (in tons). Steel production is related to the amount of labor used (4) and the amount of capital used (C) by thể 1 ng UREE S20 In this fermula Lrepresents the units of labor input and C the units of capital input. Each unit of labor conts sso, and each unit of capital costs $100. (a) Formulate an optimization problem that will determine how much labor and capital are needed in order to produce 55,000 tons of steel at minimum cost. 55,000 LCR0 (b) Solve the optimiaation problem you formulated in part (a). Hnti When using Ecel Solver, start with an initial L and Co. Rund your andwers to the nearest integer) at (.C)

Let Srepresent the amount of steel produced (in tons). Steel production is related to the amount of labor used (4) and the amount of capital used (C) by thể 1 ng UREE S20 In this fermula Lrepresents the units of labor input and C the units of capital input. Each unit of labor conts sso, and each unit of capital costs $100. (a) Formulate an optimization problem that will determine how much labor and capital are needed in order to produce 55,000 tons of steel at minimum cost. 55,000 LCR0 (b) Solve the optimiaation problem you formulated in part (a). Hnti When using Ecel Solver, start with an initial L and Co. Rund your andwers to the nearest integer) at (.C)

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter9: Production Functions

Section: Chapter Questions

Problem 9.9P

See similar textbooks

Similar questions

What is the difference between a fixed input and a variable input?
What is a production function?
What is the difference between economies of scale, constant returns to scale, and diseconomies of scale?
Let S represent the amount of steel produced (in tons). Steel production is related to the amount of labor used () and the amount of capital used () by the following function: S- 20 L0 C0.7 In this formula L represents the units of labor input and Cthe units of capital input. Each unit of labor costs $50, and each unit of capital costs $100. (a) Formulate an optimization problem that will determine how much labor and capital are needed in order to produce 50,000 tons of steel at minimum cost. If your answer is zere, enter "p" Min 40 120 s.t. 20 S0000 (b) Solve the optimization problem you formulated in part a. Hint: When using Excel Solver, start with an initial >oand C0 Do not round intermediate calculations. Round your answers to the nearest whole number 2991 2318 Cost S 397448 ide Feedback
Let S represent the amount of steel produced (in tons). Steel production is related to the amount of labor used (L) and the amount of capital used (C) by the following function. 2040.30 0.70 In this formula L represents the units of labor input and C the units of capital input. Each unit of labor costs $50, and each unit of capital costs $100. (a) Formulate an optimization problem that will determine how much labor and capital are needed in order to produce 55,000 tons of steel at minimum cost. min s.t. S = $ L, C≥ 0 = 55,000 (b) Solve the optimization problem you formulated in part (a). What is the optimal solution value (in dollars)? Hint: Use the Multistart option as described in Appendix 8.1. Add lower and upper bound constraints of 0 and 5,000 for both L and C before solving. (Round your answers to three decimal places.) at (L, C) =
Let S represent the amount of steel produced (in tons). Steel production is related to the amount of labor used (L) and the amount of capital used (C) by the following function. S = 20L 0.30c0.70 In this formula L represents the units of labor input and C the units of capital input. Each unit of labor costs $50, and each unit of capital costs $100. (a) Formulate an optimization problem that will determine how much labor and capital are needed in order to produce 55,000 tons of steel at minimum cost. Min 50L + 100C s.t. ,0.300.70 20L = 55,000 L, C 2 0 (b) Solve the optimization problem you formulated in part (a). (Hint: When using Excel Solver, start with an initial L > 0 and C > 0. Round your answers to the nearest integer.) at (L, C) = ( 2467, 2880 2$
Q1 a) Given a production function depicting the response of paddy rice tofertilizer application,Y = 3X+ 9X2 - X3(i) Calculate the exact MPP and APP.(ii) At what level of fertilizer input(X) does MPP, APP and TPP reachtheir maximum values?(iii) At what level of fertilizer input will r = 0? And what is the valueof TPP at that level?(iv) If the farmer increases the amount of fertilizer in his riceproduction in his area of diminishing returns, explain whether ornot total production will increase or decrease.
Q1 a) Given a production function depicting the response of paddy rice tofertilizer application,Y = 3X+ 9X2 - X3(i) Calculate the exact MPP and APP.(ii) At what level of fertilizer input(X) does MPP, APP and TPP reachtheir maximum values?(iii) At what level of fertilizer input will r = 0? And what is the valueof TPP at that level?(iv) If the farmer increases the amount of fertilizer in his riceproduction in his area of diminishing returns, explain whether ornot total production will increase or decrease.b) Explain the economic significance of farm records.Q2 a) What are the major objectives of agricultural marketing?b) Explain how one can evaluate the efficiency of a marketing situation.
Prof. Smith and Prof. Jones are going to produce a new textbook. The production function for the book is: ?=?1/2?1/2?= is the number of pages in the finished book?= is the number of working hours spent by Smith?= is the number of working hours spent by JonesSmith's labor is valued at 3 TL per working hour and Jones's labor is valued at 12 TL per working hour. After having spent 900 hours preparing the first draft, Smith cannot contribute any more to the book. Jones will revise the Smith's draft to complete the book.a) How many hours will Jones have to spend to produce a finished book of 300 pages?b) What is the marginal cost of the 300th page of the finished book?
You have been hired by Kia as manager for its Pakistan operations. Assume following is the short-run production function at their assembly plant outside Karachi: Q = 10L2 – 0.5 L3 where L is variable input labor, Q is output of Cars assembled 1.Find the ranges of the three stages of production. 2.Demonstrate the relationship between Total Production, Marginal Product and AverageProduct in a hypothetical graph and clearly label the three stages as per the values of Lyou observed in (a) above 3.At the end of the year it is expected that output will double with purchase ofnew equipment and machinery. The production function is estimated to be Q = 60L.30K.70 where L is labor and K is capital. Suppose initial L1 = 1 and K1 = 1. When inputs are in increased to L2 = 2 and K2 = 2, do you observe increasing, decreasing or constant returns to scale? 4.Assume Kia Head Office is considering hiring more laborers either at their Gwadarplant or…
Complete the table directly below by calculating MP and AP. Inputs ofL TP MP AP 0 01 152 343 514 655 746 807 838 82 Plot the TP, MP and AP and explain in detail the relationship between eachpair of curves. Explain why PM first rises, then declines, and ultimatelybecomes negative.
1. Consider the production function Q=K³/ª L/4 Further suppose that capital is fixed at 16 units. Answer the following questions: a. Find Q when L =16 units. What is the output (Q) when L increases to 81 units? e b. Find the average product of labor when L when L increases 81 units? 16 units. What is the average product of labor %3D c. Find the marginal product of labor when L 16 units. What is the marginal product of labor when L increases 81 units? d. Show that doubling all the inputs doubles the output.