1. **State the problem:** We need to find the break-even quantity and the number of pens to sell to achieve a monthly profit of 15000. 2. **Define variables and formulas:** Let $x$ be the number of pens sold. - Selling price per pen = 1 - Fixed cost = 25000 - Variable cost per pen = 0.5 Total cost = Fixed cost + Variable cost per pen \times number of pens = $$25000 + 0.5x$$ Total revenue = Selling price per pen \times number of pens = $$1 \times x = x$$ 3. **Break-even quantity:** Break-even occurs when total revenue equals total cost: $$x = 25000 + 0.5x$$ Subtract $0.5x$ from both sides: $$x - 0.5x = 25000$$ $$\cancel{x} - 0.5\cancel{x} = 25000$$ $$0.5x = 25000$$ Divide both sides by 0.5: $$x = \frac{25000}{0.5}$$ $$x = 50000$$ So, the break-even quantity is 50000 pens. 4. **Quantity for monthly profit of 15000:** Profit = Revenue - Cost We want profit = 15000, so: $$15000 = x - (25000 + 0.5x)$$ Simplify the right side: $$15000 = x - 25000 - 0.5x$$ $$15000 = 0.5x - 25000$$ Add 25000 to both sides: $$15000 + 25000 = 0.5x$$ $$40000 = 0.5x$$ Divide both sides by 0.5: $$x = \frac{40000}{0.5}$$ $$x = 80000$$ So, to obtain a monthly profit of 15000, 80000 pens must be sold.