The cost (in 000's) of producing x thousands of loudspeaker systems is TC = x^3 + 3x^2 - 10x + 2. Price (p) and quantity demanded (x) which are both required to be non-negative are related by p = 130 - 2x. Marginal Cost (MC) = 3x^2 + 6x - 10.
a) Find Marginal Revenue (MR) as a function of output
b) What quantity maximises revenue, and what is the corresponding revenue?
c) What quantity maximises profit, and what is the corresponding profit?