The market price of an item is $250. The Production cost, C, for a particular company is a function of its output level, q, and is given by C = 100q1.2, where C is in units of dollars and q is the number of units produced. The firm wants to maximize profit, defined as total revenue minus total cost.
(a) Determine the optimum output level to maximize profit for the firm and derive the sufficiency condition to show that the output does, in fact represent a local maximum.
(b) Arguing from the form of the objective function, what type of stationary point has been found?
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