The Scenario: Your cousin Caleb has a dog-walking business, and you'd like to start one in your own neighborhood. Caleb has had

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3 years ago

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The Scenario: Your cousin Caleb has a dog-walking business, and you'd like to start one in your own neighborhood. Caleb has had

his business for more than a year and has experimented with different prices for his services. He is willing to share what he has learned with you as you begin to plan your business. The Project: Use the information provided in the Performance Task to learn more about your competition and the costs of your business. See what you can discover by looking at Caleb's sales records to help you decide how to set up and price your own dog-walking services. Use the questions below to help you gather information and get your new business off to a profitable start. Understanding the Competition 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. (12 points: 1 point for each table cell)
Outward HoundA1-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. (6 points: 3 points for describing services, 1 point for each of the other questions)
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. (9 points: 1 point for each completed table cell)
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. (4 points: 1 point for each explanation) 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:
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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. (6 points: 1 point for each element: price, number of customers, and cost; 3 points for writing and simplifying the profit equation) 8. Now find the maximum point on the graph of your profit equation (the vertex). (5 points: 1 point for each box in part a; 2 points for part b) a. b. Substitute x into the profit function to find the maximum profit. Maximum profit: . 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.) (3 points: 1 point for price and 2 points for explanation) 10. What are the break-even points of the profit function (the values of x where profit equals 0)? Use the quadratic formula. (4 points: 2 points for each x-value) 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? (4 points: 2 points for the break-even values, and 2

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Mathematics