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 = 20L0.30c0.70 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. 20L0.300.70 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 andC > 0. Round your answers to the nearest integer.) | at (L, C) = ( 2467, 2880|)

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 = 20L0.30c0.70 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. 20L0.300.70 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 andC > 0. Round your answers to the nearest integer.) | at (L, C) = ( 2467, 2880|)

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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