Final answer:
The break-even point is achieved when 5 units are sold since this is the point where cost equals revenue, resulting in no profit or loss.
Step-by-step explanation:
The break-even point occurs when the cost C is equal to the revenue R. Given the cost function C = 15x + 150 and the revenue function R = 45x, we find the break-even point by setting them equal to each other and solving for x:
15x + 150 = 45x
To find the solution, we subtract 15x from both sides:
150 = 30x
Dividing both sides by 30 gives us:
x = 5
At x = 5, the break-even point is achieved because, at this quantity, the total costs and total revenue are the same, meaning there is neither profit nor loss.