Determine the price elasticity of demand, Microeconomics

Given the following demand and total cost functions for a firm

P = 4500 - 0.5Q2                   

TC = 1.5Q3 - 50Q2 + 1000  

i) the marginal profit function                                       

ii) the profit maximizing output level                             

iii) the price elasticity of demand, given that Q = 50 units

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