Assume the private marginal benefit from a good can be represented by the inverse demand equation, P=100−Q. Assume the private marginal cost of producing the good can be represented by the supply equation, P=3Q. If consuming the good generates a negative externality of $10 for each unit consumed, calculate:

a. The privately optimal level of consumption and production,

b. The socially optimal level of consumption and production,

c. The deadweight loss to society if no action is taken.