It helps you know if the answer is reasonable because when you do the work and get your answer, you can check if it is close to your estimate, and if it is, it is most likely correct. On the other hand if it is not close to the estimate it is most likely wrong, unless you estimated incorrectly.
Answer: 599.42 games To answer this question, you need to calculate the revenue for every game sold first. The calculation would be: Revenue= sell cost - manufacture cost= $20-$2.65= $17.35/game.
Break even is the point when the game manufacturing cost(equipment cost included) is covered by the revenue you got. Then the calculation would be:
total game cost= revenue per game * number of game sold $10400= number of game sold * $17.35 number of game sold= 10400/17.35= 599.42 games
An inflection point occurs when the second derivative changes signs. Since f"(x) is decreasing and has an x-intercept at 0, it changes signs from + to -, so there is an inflection point at x = 0.
