The cost to produce $x$ units of wire is $C=45 x+450$, while the revenue is $R=70 x$. Find all intervals where the product will t least break even.
elect the correct choice below and, if necessary, fill in the answer box to complete your choice.
Answer
Final Answer: The product will at least break even when \(x \geq \boxed{18}\).
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 \(x \geq \boxed{18}\).
