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3. [Profit maximization] If the producer's cost function is TC(q) = 200q+4.25q2, and the demand function is p = 12005.75q where p is the selling

3. [Profit maximization]

If the producer's cost function is

TC(q) = 200q+4.25q2,

and the demand function is

p = 12005.75q

where p is the selling price per unit.

(a) What output q maximizes its profit?

(b) What is the profit-maximizing price, p?

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