A company is deciding on how many factories to build. All the factories would be identical, each having the following cost function:

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A company is deciding on how many factories to build. All the factories would be identical, each having the following cost function:

ccq) = = q3 - 10 q2 + 150 q

a) At what level of production will the company be better off using two factories instead of one?

b) Derive an expression for the optimal number of factories for this firm in terms of the desired level of output q? Given this result, how many units are produced at each factory in terms of total output q? [Hint: Assume that Since the factories are identical, output will be split equally between them. So the total costs of producing an amount q using n factories will be the cost of producing / 2 at one factory times the number of factories.]

c) Find expressions for the marginal cost and average cost functions for a single factory. Graph these cost Curves. On this graph, show where the optimal number of units per factory is the number you found in part (b)).

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