radwyn horticulture is a company which focuses upon selling saplings. the company can grow a sapling for…

radwyn horticulture is a company which 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.\n|salesperson|commission/sale|\n|--|--|\n|lara|$8.15|\n|ian|$11.25|\n|ari|$8.90|\n\nradwyn horticultures 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?\n a. lara sells 221 saplings; ian sells 191 saplings; ari sells 245 saplings\n b. lara sells 221 saplings; ian sells 245 saplings, ari sells 191 saplings\n c. lara sells 191 saplings; ian sells 221 saplings, ari sells 245 saplings\n d. lara sells 191 saplings; ian sells 245 saplings, ari sells 221 saplings

radwyn horticulture is a company which 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.\n|salesperson|commission/sale|\n|--|--|\n|lara|$8.15|\n|ian|$11.25|\n|ari|$8.90|\n\nradwyn horticultures 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?\n a. lara sells 221 saplings; ian sells 191 saplings; ari sells 245 saplings\n b. lara sells 221 saplings; ian sells 245 saplings, ari sells 191 saplings\n c. lara sells 191 saplings; ian sells 221 saplings, ari sells 245 saplings\n d. lara sells 191 saplings; ian sells 245 saplings, ari sells 221 saplings

Answer

Explanation:

Step1: Calculate profit per sapling before commission

Profit per sapling before commission = Selling price - Cost price = $36.50 - 15.45=$21.05$

Step2: Set up break - even equation

Let the number of saplings sold by Lara, Ian and Ari be $x$, $y$ and $z$ respectively. The total fixed cost is $C = 7699.45$. The profit from selling saplings considering commissions is $P=(21.05 - 8.15)x+(21.05 - 11.25)y+(21.05 - 8.90)z$. At break - even, $P = 7699.45$.

Step3: Test option a

For option a: $x = 221$, $y = 191$, $z = 245$ Profit $=(21.05 - 8.15)\times221+(21.05 - 11.25)\times191+(21.05 - 8.90)\times245$ $=12.9\times221 + 9.8\times191+12.15\times245$ $=12.9\times221=2850.9$, $9.8\times191 = 1871.8$, $12.15\times245=2976.75$ $2850.9+1871.8 + 2976.75=7699.45$

Step4: Test other options (for completeness)

For option b: $x = 221$, $y = 245$, $z = 191$ Profit $=(21.05 - 8.15)\times221+(21.05 - 11.25)\times245+(21.05 - 8.90)\times191$ $=12.9\times221+9.8\times245 + 12.15\times191$ $=2850.9+2401+2320.65=7572.55\neq7699.45$

For option c: $x = 191$, $y = 221$, $z = 245$ Profit $=(21.05 - 8.15)\times191+(21.05 - 11.25)\times221+(21.05 - 8.90)\times245$ $=12.9\times191+9.8\times221+12.15\times245$ $=2463.9+2165.8+2976.75 = 7606.45\neq7699.45$

For option d: $x = 191$, $y = 245$, $z = 221$ Profit $=(21.05 - 8.15)\times191+(21.05 - 11.25)\times245+(21.05 - 8.90)\times221$ $=12.9\times191+9.8\times245+12.15\times221$ $=2463.9+2401+2685.15=7549.05\neq7699.45$

Answer:

A. Lara sells 221 saplings; Ian sells 191 saplings; Ari sells 245 saplings