In business, profit is the difference between revenue and cost; that is,
Total profit = Total revenue - Total cost,
P(x) = R(x) - C(x),
Where x is the number of units sold. Find the maximum profit and the number of units that must be sold in order to yield the maximum profit for each of the following.
a. R(x) = 5x, C(x) = 0.001x2 + 1.2x + 60
b. R(x) = 50x - 0.5x2, C(x) = 10x + 3