Radwyn Horticulture is a company that focuses upon selling saplings. The company can grow a sapling for $15.45 and can sell that sapling for $36.50. There are three main salespeople at Radwyn Horticulture, each of whom earns a different commission per sapling sold, as shown in the table below.
| Salesperson | Commission/Sale |
| :---------- | :---------------- |
| Lara | $8.15 |
| Ian | $11.25 |
| Ari | $8.90 |
Radwyn Horticulture's fixed overhead expenses last month came to $7,699.45. It is known that one salesperson sold 191 saplings, one salesperson sold 245 saplings, and one salesperson sold 221 saplings. Which arrangement of sales would cause Radwyn Horticulture to break even?
A. Lara sells 221 saplings; Ian sells 191 saplings; Ari sells 245 saplings
B. Lara sells 221 saplings; Ian sells 245 saplings, Ari sells 191 saplings
C. Lara sells 191 saplings; Ian sells 221 saplings, Ari sells 245 saplings
D. Lara sells 191 saplings; Ian sells 245 saplings, Ari sells 221 saplings
Answer (1)
Calculate the profit per sapling for each salesperson: Lara's profit is $12.90 , Ian's profit is $9.80 , and Ari's profit is $12.15 .
Calculate the total profit for each sales arrangement by multiplying the number of saplings sold by each salesperson by their respective profit and summing the results.
Compare the total profit of each arrangement to the fixed overhead expenses of $7 , 699.45 .
Determine that arrangement a (Lara sells 221, Ian sells 191, Ari sells 245) results in a total profit of $7 , 699.45 , which equals the fixed overhead expenses, thus breaking even. The answer is a
Explanation
Calculate Profit per Sapling First, we need to calculate the profit each salesperson generates per sapling sold. This is the selling price minus the cost to grow the sapling and the salesperson's commission.
Lara's Profit Lara's profit per sapling is calculated as follows: 36.50 − 15.45 − 8.15 = 12.90 So, Lara makes $12.90 profit per sapling.
Ian's Profit Ian's profit per sapling is: 36.50 − 15.45 − 11.25 = 9.80 Thus, Ian makes $9.80 profit per sapling.
Ari's Profit Ari's profit per sapling is: 36.50 − 15.45 − 8.90 = 12.15 Therefore, Ari makes $12.15 profit per sapling.
Check Each Arrangement Now, we need to check each arrangement to see which one results in the company breaking even. Breaking even means the total profit equals the fixed overhead expenses, which are $7 , 699.45 .
Arrangement a Arrangement a: Lara sells 221, Ian sells 191, Ari sells 245. Total profit is: ( 221 × 12.90 ) + ( 191 × 9.80 ) + ( 245 × 12.15 ) = 2850.90 + 1871.80 + 2976.75 = 7699.45 Since the total profit is $7699.45 , this arrangement results in breaking even.
Arrangement b Arrangement b: Lara sells 221, Ian sells 245, Ari sells 191. Total profit is: ( 221 × 12.90 ) + ( 245 × 9.80 ) + ( 191 × 12.15 ) = 2850.90 + 2401.00 + 2310.65 = 7562.55 Since the total profit is not equal to $7699.45 , this arrangement does not result in breaking even.
Arrangement c Arrangement c: Lara sells 191, Ian sells 221, Ari sells 245. Total profit is: ( 191 × 12.90 ) + ( 221 × 9.80 ) + ( 245 × 12.15 ) = 2463.90 + 2165.80 + 2976.75 = 7606.45 Since the total profit is not equal to $7699.45 , this arrangement does not result in breaking even.
Arrangement d Arrangement d: Lara sells 191, Ian sells 245, Ari sells 221. Total profit is: ( 191 × 12.90 ) + ( 245 × 9.80 ) + ( 221 × 12.15 ) = 2463.90 + 2401.00 + 2685.15 = 7550.05 Since the total profit is not equal to $7699.45 , this arrangement does not result in breaking even.
Conclusion Therefore, only arrangement a results in Radwyn Horticulture breaking even.
Examples
Understanding break-even points is crucial in business. For example, a small bakery needs to know how many cakes they must sell each month to cover their rent, ingredients, and staff salaries. By calculating the cost to produce each cake and the selling price, they can determine the exact number of cakes needed to break even. This concept extends to larger companies as well, helping them make informed decisions about pricing, production levels, and sales targets to ensure profitability.
