1. **Problem Statement:** We have break-even diagrams for two businesses, A and B, showing fixed costs, variable costs, total costs, and revenue against output units. We need to identify: - The area of profit and loss on the first graph. - For Business A and B, identify: (i) The most favourable break-even point in units. (ii) The lowest fixed cost. (iii) The highest sales price per unit. (iv) The lowest variable cost per unit. 2. **Understanding Break-Even Diagrams:** - Fixed costs are constant regardless of output. - Variable costs increase linearly with output. - Total costs = Fixed costs + Variable costs. - Revenue increases linearly with output. - Break-even point is where total costs = revenue. - Profit area is where revenue > total costs. - Loss area is where total costs > revenue. 3. **Identifying Profit and Loss Areas (Question 3):** - Profit area: Output units greater than break-even point where revenue line is above total costs line. - Loss area: Output units less than break-even point where total costs line is above revenue line. 4. **Business A and B Analysis (Question 4):** (i) **Most favourable break-even point:** The business with the lower break-even output units. - From the graphs, find the output where revenue = total costs for each business. (ii) **Lowest fixed cost:** The business with the lower fixed cost line (constant value). (iii) **Highest sales price per unit:** Sales price per unit = slope of revenue line = (Revenue change) / (Output change). (iv) **Lowest variable cost per unit:** Variable cost per unit = slope of variable cost line = (Variable cost change) / (Output change). 5. **Calculations:** - Let $x$ be output units. For Business A: - Break-even point $x_A$ where revenue = total costs. - Fixed cost $F_A$ is the constant fixed cost line value. - Sales price per unit $p_A = \frac{\Delta \text{Revenue}}{\Delta x}$. - Variable cost per unit $v_A = \frac{\Delta \text{Variable Cost}}{\Delta x}$. For Business B: - Break-even point $x_B$ where revenue = total costs. - Fixed cost $F_B$. - Sales price per unit $p_B$. - Variable cost per unit $v_B$. 6. **From the graphs (approximate values):** - Business A break-even at about 150 units. - Business B break-even at about 100 units. - Fixed costs: Business A higher than Business B. - Sales price per unit: Calculate slope of revenue line. For Business A: Revenue rises from 0 to 1400 for 0 to 250 units, so $p_A = \frac{1400}{250} = 5.6$. For Business B: Revenue rises similarly, $p_B = \frac{1400}{250} = 5.6$. - Variable cost per unit: For Business A: Variable cost rises from 0 to about 700 for 0 to 250 units, so $v_A = \frac{700}{250} = 2.8$. For Business B: Variable cost rises from 0 to about 500 for 0 to 250 units, so $v_B = \frac{500}{250} = 2$. 7. **Answers:** (i) Most favourable break-even point: Business B (100 units < 150 units). (ii) Lowest fixed cost: Business B (lower fixed cost line). (iii) Highest sales price per unit: Both equal at 5.6. (iv) Lowest variable cost per unit: Business B (2 < 2.8). **Final summary:** - Profit area is where revenue line is above total costs line (output > break-even). - Loss area is where total costs line is above revenue line (output < break-even). - Business B has the most favourable break-even point, lowest fixed cost, and lowest variable cost per unit. - Both businesses have the same sales price per unit.