Firm''s profit function, Econometrics

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A  firm manufactures  and  sells  a  product  that  has  the  following  demand function:
 
   
Q = 180 - 4P
 
where P  is price, Q  is quantity.  It also  faces  the  following  total cost  (TC) function:

 TC =0.033Q2 + 15Q+150
 
where Q is quantity produced.
 
    
(i)  Determine the firm's profit function.

(ii)  Using your profit function measured in part (i) find the level of output where the firm maximises its profit.


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