Final answer:
To break even, Michael needs to increase the number of units sold by approximately 6.68%. This is calculated based on his total costs and total revenue, considering his variable costs per item, fixed costs, and the average price at which he sells his items.
Step-by-step explanation:
To determine the percentage increase in the number of units sold required for Michael to break even, we'll first calculate his total cost and then his total revenue at the current level of sales. We'll use the break-even point formula, where total costs equal total revenue.
First, let's calculate total costs: Michael's total costs include variable costs and fixed costs. The variable cost is the cost to harvest his indigreens, which amounts to $9 per item. Given that he sold 2,500 items last year, the total variable cost equates to 2,500 items × $9/item = $22,500. Michael also has fixed costs of $8,000 per year. Thus, the total cost is $22,500 + $8,000 = $30,500.
Then, calculate total revenue: At an average price of $12 per item and 2,500 items sold, total revenue is 2,500 items × $12/item = $30,000.
Now, we need to determine how many additional units Michael must sell at $12 per item to cover the extra $500 ($30,500 total cost – $30,000 total revenue) needed to break even. Since his cost per item is $9, the profit per additional item sold is $12 - $9 = $3. Therefore, he needs to sell an additional $500 / $3 per item = approximately 167 items to break even.
To find the percentage increase in the number of units sold, we take the additional units required to break even and divide it by the original amount of units sold, then multiply by 100. That's 167 items / 2,500 items × 100 = approximately 6.68%.
Thus, Michael needs to increase his sales by approximately 6.68% to break even.