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Question #42146
The production function for a product is given by Q=100KL. If the price of labor is $30 per day and the price of capital is$20 per day, what is the minimum cost of producing 1000 units of output? Use alternatively three methods (substitution, equal slopes, and lagrange) to solve the problem.
If&nbsp;production function for a product is given by Q=100KL and Q = 1000 units, so 100KL = 1000, KL = 10
As the&nbsp;price of labor is $30 per day and the price of capital is$20 per day, the cost will be minimal, if we use less labor and more capital, so K = 10, L = 1

So, the minimum cost will be TCmin = 30*1+ 20*10 = \$230.

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