1. **Problem Statement:** A publishing company has a cost of Le 0.38 per copy and revenue of Le 0.35 per copy. Dealers get Le 0.3 of the revenue. Advertising revenue is 10% of dealer revenue for copies sold beyond 10,000 units. Find the least number of copies to sell for a positive profit. 2. **Define variables:** Let $x$ be the number of copies sold. 3. **Calculate dealer revenue:** Dealer revenue per copy is $0.3 \times 0.35 = 0.105$ Le. 4. **Calculate advertising revenue:** Advertising revenue applies only for copies beyond 10,000, so for $x > 10,000$, advertising revenue is $10\%$ of dealer revenue on those copies: $$\text{Advertising revenue} = 0.10 \times 0.105 \times (x - 10,000) = 0.0105(x - 10,000)$$ 5. **Total revenue:** Revenue from copies sold is $0.35x$. 6. **Total cost:** Cost per copy is $0.38x$. 7. **Profit formula:** Profit = Total revenue + Advertising revenue - Cost - Dealer's share Dealer's share is $0.105x$ (from step 3). So, $$\text{Profit} = 0.35x + 0.0105(x - 10,000) - 0.38x - 0.105x$$ Simplify: $$= 0.35x + 0.0105x - 105 - 0.38x - 0.105x$$ $$= (0.35 + 0.0105 - 0.38 - 0.105)x - 105$$ $$= (-0.1245)x - 105$$ 8. **Set profit > 0 for positive profit:** $$-0.1245x - 105 > 0$$ $$-0.1245x > 105$$ $$x < -\frac{105}{0.1245}$$ Since $x$ cannot be negative, this means no positive profit is possible under these conditions. 9. **Re-examine the problem:** The advertising revenue is an additional income, so it should be added to revenue, not subtracted. The dealer's share is part of revenue paid out, so cost includes cost per copy plus dealer's share. Recalculate profit as: $$\text{Profit} = \text{Revenue} + \text{Advertising revenue} - \text{Cost} - \text{Dealer's share}$$ But dealer's share is part of revenue, so better to write: $$\text{Profit} = (\text{Revenue} - \text{Dealer's share}) + \text{Advertising revenue} - \text{Cost}$$ Dealer's share = $0.105x$, revenue after dealer = $0.35x - 0.105x = 0.245x$ Profit: $$= 0.245x + 0.0105(x - 10,000) - 0.38x$$ $$= 0.245x + 0.0105x - 105 - 0.38x$$ $$= (0.255 - 0.38)x - 105$$ $$= -0.125x - 105$$ Again negative slope, no positive profit. 10. **Conclusion:** Since cost per copy (0.38) is greater than net revenue per copy (0.245), the company cannot make a positive profit regardless of copies sold. **Final answer:** No positive profit is possible under the given conditions.