Question

A company charges $200 for each leather bag on order of 150 or less. The cost of each bag is reduced by $1 for each order in excess of 150 pieces. How many bags on order would result in maximum revenue? What is the maximum revenue?

Answer 1

the price, for n >= 150, is

p(n) = 200-n

Revenue is price*quantity, so

r(n) = n(200-n) = 200n-n^2

That's just a parabola. The vertex is the point of maximum revenue. That's just algebra I, so no sweat.
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right?