1. Explore the three competitors in your area to learn more about the services they offer and how they reach their customers. Fill in the table below to help you compare their businesses. Outward Hound
A1-Pet Services
Debbie's Daily Dog Walks
What services does the business offer?
What do you know about the type of business and its staff?
Who are the target customers?
How much does the business charge?
2. Now that you know a bit about the competition, it's time to get more specific about your business offering.
List three services you would like to offer.
Do any of these services require you to buy special items? If so, what would you need to buy?
Describe the type of customer you believe your business will appeal to and explain why.
If you had to guess now, how much do you think you should charge for a 30-minute dog walk?
Calculating Your Business Costs
3. Use the table below to summarize your monthly business costs. Record each option you choose in the "Options selected" column.
Cost type
Total cost per month
Options selected
Advertising
Goods
Transportation
Licensing
TOTAL
4. Explain the choices you made that determined your business costs in each cost category.
In your explanation, be sure to describe:
❑ Your advertising choices
❑ The goods you will purchase
❑ Your transportation needs
❑ Whether you chose bonding
❑ The reasons for your choices
Advertising:
Goods:
Transportation:
Bonding:
Investigating Sales Records
5. Based on the sales data Caleb sent you, answer the questions below to find the relationship between the change in customers per month and a $1 change in price.
Price per 30 min
Customers per month
Revenue per month
$12
214
$5136
$14
202
$5656
$18
178
$6408
$22
154
$6776
$28
118
$6608
$34
82
$5576
Using Caleb's data, give an example of a price increase and an example of a price decrease. Include the change in the number of customers with each example.
Price Increases
• If Caleb increased his price from to , the price increased by and the number of customers (increased/decreased) by .
Price Decreases
• If Caleb decreased his price from to , the price decreased by and the number of customers (increased/decreased) by .
• With every price increase of $1, Caleb (gained/lost) customers.
• With every price decrease of $1, Caleb (gained/lost) customers.
6. Write a profit equation for Caleb's business.
Profit = Price • Number of customers – Cost
To write the profit equation, use the following assumptions:
❏ Express price and number of customers in terms of the same variable, x.
❏ Let x = the change in price from the price that gave Caleb the greatest revenue.
Use the information in the table to answer these questions. (9 points: 1 point per blank)
a. At what price did Caleb make the most revenue per month? How many customers did he serve at that price?
Price:
Number of customers:
b. Write an expression for price. Use the price identified in part a. Let x represent the change in Caleb's price from this price.
Price = +
c. Write an expression for the number of customers. Use the number of customers identified in part a, and the decrease in number of customers when Caleb increases his price by $1 (from question 5).
Number of customers = – x
d. Write Caleb's profit equation. Use the expressions you identified in parts b and c. Assume Caleb's costs amounted to $200 each month.
Profit = Price • Number of customers – Cost
Profit = • –
Maximizing Your Profits
You've done a lot of research. Now it's time to try to maximize the profit of your new business.
7. Write and simplify your personalized profit equation.
Complete the profit equation, using the price and customer expressions from question 6 and your total cost from question 3.
8. Now find the maximum point on the graph of your profit equation (the vertex).
a.
b. Substitute x into the profit function to find the maximum profit.
Maximum profit:
9. According to your model, what price should you charge to maximize profit? Explain how you know this is the best price. (Hint: Remember that x represents change in price from $22, not price.)
10. What are the break-even points of the profit function (the values of x where profit equals 0)? Use the quadratic formula.
11. According to your model, between what two prices should you price your service? Why would you want to keep your price between those limits?
12. Sketch a graph of your profit function.
Vertex:
x-intercepts: and