Radwyn Horticulture is a company which focuses upon selling saplings. The company can sell a sapling for $36.50. There are three main salespeople at Radwyn Horticulture who each earn a different commission per sapling sold, as shown in the table below.
| Person | 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 of 657 saplings, one salesperson sold 191 saplings, one salesperson sold 245 saplings, and one salesperson sold 221 saplings. Which 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 (2)
Calculate the total revenue: 36.50 × 657 = $23980.50 .
Calculate the total cost for each sales distribution by summing the fixed overhead and the total commission.
Distribution 1: Total Cost = $13829.85
Distribution 2: Total Cost = $13956.75
Distribution 3: Total Cost = $13922.85
Distribution 4: Total Cost = $13979.25
Check which distribution results in Total Cost = Total Revenue. None of the distributions result in the company breaking even, so the answer is that none of the provided options result in a break-even scenario. None of the above
Explanation
Problem Analysis First, let's analyze the problem. We are given the selling price of each sapling, the commission rates for three salespeople (Lara, Ian, and Ari), the fixed overhead expenses, and the number of saplings sold by the three salespeople. We need to find the sales distribution among the salespeople that would cause Radwyn Horticulture to break even. Breaking even means that the total revenue equals the total costs (fixed overhead plus total commissions).
Calculate Total Revenue The company sells each sapling for 36.50. T h e t o t a l n u mb ero f s a pl in g sso l d i s 191 + 245 + 221 = 657. T h ere f ore , t h e t o t a l re v e n u e i s : 36.50 per sapling × 657 saplings = $23980.50 $
Analyze Sales Distributions Now, let's consider the four possible sales distributions and calculate the total commission and total cost for each distribution. The fixed overhead expense is $7,699.45.
Distribution 1: Commission and Cost Distribution 1: Lara sells 221, Ian sells 191, Ari sells 245. Total Commission = ( 221 × 8.15 ) + ( 191 × 11.25 ) + ( 245 × 8.90 ) = 1801.15 + 2148.75 + 2180.50 = $6130.40 Total Cost = Fixed Overhead + Total Commission = 7699.45 + 6130.40 = $13829.85
Distribution 2: Commission and Cost Distribution 2: Lara sells 221, Ian sells 245, Ari sells 191. Total Commission = ( 221 × 8.15 ) + ( 245 × 11.25 ) + ( 191 × 8.90 ) = 1801.15 + 2756.25 + 1699.90 = $6257.30 Total Cost = Fixed Overhead + Total Commission = 7699.45 + 6257.30 = $13956.75
Distribution 3: Commission and Cost Distribution 3: Lara sells 191, Ian sells 221, Ari sells 245. Total Commission = ( 191 × 8.15 ) + ( 221 × 11.25 ) + ( 245 × 8.90 ) = 1556.65 + 2486.25 + 2180.50 = $6223.40 Total Cost = Fixed Overhead + Total Commission = 7699.45 + 6223.40 = $13922.85
Distribution 4: Commission and Cost Distribution 4: Lara sells 191, Ian sells 245, Ari sells 221. Total Commission = ( 191 × 8.15 ) + ( 245 × 11.25 ) + ( 221 × 8.90 ) = 1556.65 + 2756.25 + 1966.90 = $6279.80 Total Cost = Fixed Overhead + Total Commission = 7699.45 + 6279.80 = $13979.25
Check for Breakeven Now, we check which distribution results in the total cost equaling the total revenue ($23980.50). Distribution 1: $23980.50 - $13829.85 = 10150.65 = 0 Distribution 2: $23980.50 - $13956.75 = 10023.75 = 0 Distribution 3: $23980.50 - $13922.85 = 10057.65 = 0 Distribution 4: $23980.50 - $13979.25 = 10001.25 = 0 None of the distributions result in the company breaking even.
Final Answer Since none of the given sales distributions result in the total cost equaling the total revenue, none of them would cause Radwyn Horticulture to break even.
Examples
Understanding break-even points is crucial in business. For example, a small bakery can use this concept to determine how many cakes they need to sell each month to cover their rent, ingredient costs, and employee wages. By calculating their fixed costs (rent, wages) and variable costs (ingredients per cake), they can find the exact number of cakes needed to be sold to break even. This helps them make informed decisions about pricing, production, and overall business strategy to ensure profitability.
After calculating total revenue and costs for each sales distribution, none of the distributions allow Radwyn Horticulture to break even since total costs exceed total revenue in all cases.
;
