Subjects algebra

Break Even Point

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Break Even Point


1. **State the problem:** We need to find the break-even point where revenue equals cost. 2. **Define variables:** Let $x$ be the number of items. 3. **Write the revenue function:** Revenue per item is 25, so total revenue is $$R(x)=25x$$. 4. **Write the cost function:** Fixed cost is 2100 plus 10 per item, so total cost is $$C(x)=2100+10x$$. 5. **Set revenue equal to cost to find break-even:** $$25x=2100+10x$$. 6. **Solve for $x$:** $$25x-10x=2100$$ $$15x=2100$$ $$x=\frac{2100}{15}=140$$. 7. **Find the revenue (or cost) at $x=140$:** $$y=25\times140=3500$$. 8. **Write the break-even point as an ordered pair:** $$(140,3500)$$. **Final answer:** The break-even point is $(140,3500)$.