(a)  Derive the first order condition showing how much labor and capital a producer should use to minimize the total costs of producing a given level of output.

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    (a)  Derive the first order condition showing how much labor and capital a producer should use to minimize the total costs of producing a given level of output.

    (b)  What is the second order condition for the producer to achieve (a).

    (c)  Draw a figure showing your answer to part (a) and another figure showing the opposite (i.e., a producer maximizing output with given total costs). How does either situation compare with a producer who has neither a total output constraint or a total cost constraint?

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