Question

9. You are selling x un its of a product. The fixed costs for this product are $47500 and the variable costsare $65.25 per unit. You plan to see the product for $85.50 per unit.A. Find an equation for the total cost of selling x units.B. Find an equation for the total revenue for selling x units.C. Find an equation for the total profit for selling x units.D. Find the break even point. Be sure to show your work. Round to an appropriate whole number.E. How many units do you need to sell to earn a profit of $100,000? Round to an appropriate wholenumber.F. If you sell 1400 urnes, how much profit do you earn?

Answer 1

$\begin{gathered} \text{Fixed costs=\ 47,500} \\ \text{variable costs=\ 65.25} \\ Selling\text{ price = \ 85.50} \\ A\text{.} \\ Cost=\text{65.25x}+\text{47,500} \\ \text{The total cost equation is }Cost=\text{65.25x}+\text{47,500} \\ \\ B\text{. } \\ \text{Total revenue=}85.5x \\ \text{The total revenue equation is Total revenue=}85.5x \\ \\ C\text{. Profit =Total revenue for selling - total cost} \\ \text{Profit}=85.5x-(\text{65.25x}+\text{47,500}) \\ \text{Profit}=85.5x-65.25x-47,500 \\ \text{Profit =20.25x-47,500} \\ \text{The total profit equation is Profit =20.25x-47,500} \\ \\ D\text{.} \\ Break\text{ even point=}\frac{\text{Fixed costs}}{Selling\text{ price}-\text{variable costs}} \\ \\ Break\text{ even point=}\frac{\text{47,500}}{\text{85.50}-\text{65.25}} \\ \\ Break\text{ even point=}2,346 \\ \text{The break even point is 2,346 units} \\ \\ E\text{.} \\ \text{Profit =20.25x-47,500} \\ \text{Solving x} \\ x=\frac{Profit\text{ +47,500}}{20.25} \\ Profit\text{ = \ 100,000} \\ x=\frac{100,000\text{ +47,500}}{20.25} \\ x=7,284 \\ \text{You n}eed\text{ to sell 7,249 units to earn \ 100,000} \\ \\ F\text{.} \\ x=1,400 \\ \text{The units sold are under the breake even point, hence you wont earn} \\ \text{Profit =20.25(1,400)-47,500} \\ \text{Profit}=-19,150 \\ \text{The negative number says that you wont earn} \end{gathered}$