Problem

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.

Solution

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 \(x \geq \boxed{18}\).

From Solvely APP
Source: https://solvelyapp.com/problems/46299/

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