Aas QUESTION 1 The information regarding the activities of lion ine and the commercial goods it trades is as follows Unit Sales Price 100 Unit Buying Price: 34 Unit Sales Premium 6 Annual Rent Cost 150.000 Annual Salaries 350.000 Annual Advertisement Cost 100.000 1-Calculate the break-even point activity and break-even point sales in Dollars. 2-Calculate how manyunits the business needs to tell in order to earn 20% operating income on sales revenue

To solve this problem, we need to calculate the break-even point in units and sales dollars, as well as determine how many units need to be sold to achieve a 20% operating income on sales revenue.<br /><br />### 1. Break-Even Point Calculation<br /><br />**Break-Even Point in Units:**<br /><br />The break-even point in units is calculated using the formula:<br /><br />\[<br />\text{Break-Even Point (Units)} = \frac{\text{Fixed Costs}}{\text{Unit Contribution Margin}}<br />\]<br /><br />Where:<br />- Fixed Costs = Annual Rent Cost + Annual Salaries + Annual Advertisement Cost<br />- Unit Contribution Margin = Unit Sales Price - Unit Buying Price - Unit Sales Premium<br /><br />First, calculate the fixed costs:<br /><br />\[<br />\text{Fixed Costs} = \$150,000 + \$350,000 + \$100,000 = \$600,000<br />\]<br /><br />Next, calculate the unit contribution margin:<br /><br />\[<br />\text{Unit Contribution Margin} = \$100 - \$34 - \$6 = \$60<br />\]<br /><br />Now, calculate the break-even point in units:<br /><br />\[<br />\text{Break-Even Point (Units)} = \frac{\$600,000}{\$60} = 10,000 \text{ units}<br />\]<br /><br />**Break-Even Point in Sales Dollars:**<br /><br />The break-even point in sales dollars is calculated by multiplying the break-even point in units by the unit sales price:<br /><br />\[<br />\text{Break-Even Point (Sales Dollars)} = 10,000 \times \$100 = \$1,000,000<br />\]<br /><br />### 2. Units Needed for 20% Operating Income on Sales Revenue<br /><br />To find out how many units need to be sold to achieve a 20% operating income on sales revenue, we first need to define the desired operating income:<br /><br />Operating Income = 20% of Sales Revenue<br /><br />Let \( x \) be the number of units sold. Then:<br /><br />\[<br />\text{Sales Revenue} = x \times \$100<br />\]<br />\[<br />\text{Operating Income} = 0.20 \times (\text{Sales Revenue})<br />\]<br /><br />Operating Income is also equal to Total Contribution Margin minus Fixed Costs:<br /><br />\[<br />\text{Operating Income} = (x \times \text{Unit Contribution Margin}) - \text{Fixed Costs}<br />\]<br /><br />Equating the two expressions for Operating Income:<br /><br />\[<br />0.20 \times (x \times \$100) = (x \times \$60) - \$600,000<br />\]<br /><br />Simplify and solve for \( x \):<br /><br />\[<br />0.20 \times 100x = 60x - 600,000<br />\]<br />\[<br />20x = 60x - 600,000<br />\]<br />\[<br />600,000 = 40x<br />\]<br />\[<br />x = \frac{600,000}{40} = 15,000 \text{ units}<br />\]<br /><br />Therefore, the business needs to sell 15,000 units to earn a 20% operating income on sales revenue.