Show that the maximum profit occurs when the marginal revenue equals the marginal cost.
I'm pretty sure this is supposed to be some sort of proof, but I have no idea how to even start it...
r = Revenue
c = cost
p = profit = r-c
u = number of units sold
dr/du = marginal revenue
dc/du = marginal cost
so
dp/du = dr/du - dc/du = marginal profit
at peak profit, changer in profit for another unit sold is zero
so
0 = dr/du-dc/du
or
dr/du = dc/du