Imagine that you own a small business and that you have to decide how much of your product to sell every year, and which technology to use to produce it.
Your market research suggests that the price at which you will be able to sell each unit of your product is given by 200−q, where q denotes the total amount sold over the course of the year.
You have access to two different technologies, which you can use in any feasible combination. The technologies have different cost properties. Producing q units with the first technology costs 100q. Producing q units with the second technology costs q2.
QUESTION. How many units should be produced using the first technology at the profit maximizing decision?