Question

prices - additional practice
formula: (total variable costs) / (1 - .profit) = price of product

1. you are trying to sell shoes that you recently designed and manufactured. you spent $15.00 in materials to make the shoes, $9.99 to ship the shoes to stores, and paid your employee for 2 hours of labor, with an hourly rate of pay at $16.50. youre attempting to make 25% in profit. using the prices formula, what is the appropriate price for the shoes? be sure to show your work - show the formula, your numbers, and highlight or circle your final answer.
2. a friend of yours is selling burritos on the weekend as a street vendor. he asked you to help with setting a price. your friend spent $50 in ingredients, $5.00 in shipping (gas) costs to his stand, and did not have any labor costs, as he worked to make them himself - he was able to make a batch of 30 burritos. your friend would like to make 50% in profit. what is the right price per burrito? be sure you show your work - show the formula, your numbers, and highlight or circle your final answer. hint: for this one, you are getting a total price for the entire batch of 30 burritos. when you do your calculations, be sure to take the extra step and divide that total price by 30 to get a price per burrito.
3. you are working for a used car dealership, and are learning how to price cars for sale. the dealership recently acquired a subaru wrx and your boss wants you to give it a price. the dealership bought the subaru from a private owner for $15,000 (hint: this will count as your variable costs in this case). theyre paying you a salary of $20 an hour and you are spending a full days work (8 hours) on preparing this car for sale. the dealership would like to make a 15% profit on the sale of the car. what is the appropriate price for this car? be sure you show your work - show the formula, your numbers, and highlight or circle your final answer.

Explanation:

Step1: Calculate total variable costs for shoes

Materials cost is $15$, shipping cost is $9.99$, and labor cost is $2\times16.50 = 33$. So total variable costs $C_{shoes}=15 + 9.99+33=57.99$. Profit percentage $p_{shoes}=0.25$. Using the formula $P=\frac{C}{1 - p}$, where $P$ is price, $C$ is total variable costs and $p$ is profit rate. Then $P_{shoes}=\frac{57.99}{1 - 0.25}=\frac{57.99}{0.75}=77.32$.

Step2: Calculate total variable costs for burritos

Ingredients cost is $50$ and shipping cost is $5$, so total variable costs $C_{burritos}=50 + 5=55$. Profit percentage $p_{burritos}=0.5$. Total price for batch $P_{batch}=\frac{55}{1 - 0.5}=\frac{55}{0.5}=110$. Price per burrito $P_{per - burrito}=\frac{110}{30}\approx3.67$.

Step3: Calculate total variable costs for car

Purchase cost is $15000$, labor cost is $20\times8 = 160$. So total variable costs $C_{car}=15000+160 = 15160$. Profit percentage $p_{car}=0.15$. Using the formula $P=\frac{C}{1 - p}$, we get $P_{car}=\frac{15160}{1 - 0.15}=\frac{15160}{0.85}\approx17835.29$.

Answer:

1. The price of the shoes is $\$77.32$.
2. The price per burrito is approximately $\$3.67$.
3. The price of the car is approximately $\$17835.29$.