8. 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 = 20L0.30C0.70In 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 $100.(a) Formulate an optimization problem that will determine how much labor and capital are needed in order to produce 60,000 tons of steel at minimum cost.Mins.t.= 60,000%3DL, C2 0(b) Solve the optimization problem you formulated in part (a). (Hint: When using Excel Solver, start with an initial L > 0 and C > 0. Round your answers to the nearest integer.)$at (L, C)

S = 20L0.30c0.70 his 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. Formulate an optimization problem that will determine how much labor and capital are needed in order to produce 60,000 tons of steel at minimum Min s.t. = 60,000 L, C 2 0 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 answer

S = 20L0.30c0.70 his 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. Formulate an optimization problem that will determine how much labor and capital are needed in order to produce 60,000 tons of steel at minimum Min s.t. = 60,000 L, C 2 0 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 answer

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter9: Production Functions

Section: Chapter Questions

Problem 9.3P

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