I realize this is a lot to ask, but I'd be REALLY grad if someone could help me with these...

1. a)Find the level of output Q at which profit P is maximized, given the total revenue R=500Q-3Q^2 and the total cost C=5000+150Q
b) define break-even points'
c) find marginal revenue at a value of Q, where P is maximized
d) define marginal cost at the same value of Q

2. a) Find the level of output Q at which cost C is minimized, given the total cost C=500-0.1Q^2+0.001Q^3
b) find marginal cost at a value of Q, where C is minimized
c) define average cost per unit at the same value of Q
d) define total average cost, if production changes from Q=20 to Q=40

3. Given the demand function P(d) = 510-3Q-0.1Q^2 and the supply function P(s)=5+Q+Q^2 and assuming pure competition, find
a) the consumer's surplus and
b) the producer's surplus

4. a) Find the demand function Q(P) if the point elasticity is
E=-2P^2 / Q^2 for all P>0, Q>0 and Q=60 when P=30\
b) define the domain of the function Q(P)