Step 1 :Let's denote the number of units of wire produced and sold as 'x'.
Step 2 :The total cost of production C(x) is given by the equation \(C(x) = 45x + 450\).
Step 3 :The revenue function R(x) is given by the equation \(R(x) = 70x\).
Step 4 :The break-even point is the point at which total cost equals total revenue, so we need to find the value of 'x' for which \(C(x) = R(x)\).
Step 5 :Setting the two equations equal to each other gives us the equation \(45x + 450 = 70x\).
Step 6 :Subtracting 45x from both sides gives us \(450 = 25x\).
Step 7 :Dividing both sides by 25 gives us \(x = 18\).
Step 8 :Final Answer: The product will at least break even when \(x \geq \boxed{18}\).