The problem describes an electronic equipment manufacturer, Dynamo Electric, Inc., that produces surge protectors. We are given the fixed costs, the wholesale price per unit, and the manufacturing cost per unit. We have already determined the functions for the monthly total costs, monthly total revenue, and monthly profit. The final part asks us to find the number of surge protectors Dynamo must produce and sell each month to break even.

1. Problem Description

The problem describes an electronic equipment manufacturer, Dynamo Electric, Inc., that produces surge protectors. We are given the fixed costs, the wholesale price per unit, and the manufacturing cost per unit. We have already determined the functions for the monthly total costs, monthly total revenue, and monthly profit. The final part asks us to find the number of surge protectors Dynamo must produce and sell each month to break even.

2. Solution Steps

To break even, the monthly profit $P(x)$ must be equal to zero. The profit function is given by $P(x) = 6.50x - 1040$. We need to solve for $x$ when $P(x) = 0$.

$6.50x - 1040 = 0$

$6.50x = 1040$

$x = \frac{1040}{6.50}$

$x = 160$

3. Final Answer

160