# Lagrangian function

The user capital in fact is 3% and not 3$. I don't know...3% of what? Please provide me with detailed step-by-step solutions thanks.

A firm wants to minimize cost subject to its production function. Its labor cost is 10$ per person-hours and the user cost of capital is 3%. The firm wants to produce 50 units of output with the following production function 2K0.5L0.5. Use the Lagrangian function to derive how many units of capital and labor the firm should use in order to minimize costs.

See attached file for full problem description.

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#### Solution Summary

This posting uses the Lagrangian function to derive how many units of capital and labor the firm should use in order to minimize costs.

$2.19