Directions: Complete each of the tasks outlined below.
Task 1
You want to start a summer business to earn money. What will you do? You have to consider how much money you can afford to invest in this business, how much it will cost you to make each item, and how much you’re going to charge for each item. Research something that would be reasonable to make and sell with the startup investment you have determined. Example: A lemonade stand.
⦁ What is the total amount of money you are willing to invest in this business? (Example: $8.00 for the recipe)
⦁ What item are you going to make and sell? Why? (Example: Cups of Lemonade)
⦁ Describe how your business will work.
⦁ How much will it cost you to make each item?
⦁ How much will you sell each item for?
⦁ Do you think your business will be profitable? Explain your answer.
Task 2
In Task 1 you determined how much of your own money you’re willing to spend to get your business started. This is your limit—when making your product you can’t exceed this amount.
⦁ Write an inequality that represents the fact that while making your product you can’t exceed this spending limit. (If I invested $200 to start, the cost per item is less than or equal the total money you have to invest, for example if the cups of lemonade cost $.63 per cup: .63c ≤ 200 [.63 cents per cup is less than or equal to $200])
⦁ Solve this inequality and graph the solution on a number line. Example: .63c ≤ 200 or c ≤ 317.4, so I can only make 317 cups with my $200 (317 instead of 317.4 because you can’t make .4 cups)
⦁ Explain what your solution means in terms of the situation. Example: so I can only make 317 cups with my $200 (317 instead of 317.4 because you can’t make .4 cups)
⦁ In Task 1 you determined how much you will charge for each item. Write an equation that represents your total earnings based on the price of your item and how many you sell. Example: If I charge $1.50 per cup, and it costs .63 per cup to make - 1.50c - .63c = total earnings. If I sell 50 cups: 1.50(50) - .63(50) = 43.50.
⦁ Using your answer from part B and your equation from part C, what is the most money you can hope to earn from your business? SHOW THE EQUATION Example: What will be your total profit based on how many items you can sell, depending on what you invest: 1.50(317) - .63(317) = 275.79
⦁ Don’t forget that at the beginning of the process you had to spend some of your own money to get started. With the costs taken into account, what was your total profit? Did you make money or lose money? If so, how? Example: I only invested $8 to start, so $275.79 - $8 = 276.79, so I made a profit of $276.79.
⦁
Task 3
Your parents heard about the success of your business and they want to help you out. Suppose they want to give you an additional $300 to put toward your business. However, there’s a catch. If you make more than $600 total, you have to give them 10% of your earnings above $600. For example, if you have earned $650, then you owe 10% of $50, or $5, to your parents.
⦁ Now that you have an additional $300, revise your inequality from part A of Task 2 to reflect your new spending limit. Example: Add $300 to the total amount you had to spend $200 + $300 = $500, so .63c ≤ 500.
⦁ Solve this inequality. Explain what your solution means in terms of the situation. Example: .63c ≤ 500, c = 793.65, so I can sell 793 cups of lemonade.
⦁ If you still sell your item for the same price, what is the most money you can hope to earn from your business now? Example: 1.50(793) - .63(793) = $395.87
⦁ Will you have to pay your parents? If so, determine how much you will owe them. Example: 10% of whatever you make over $600. If I made $780, 780-600 = 280. 10% of 280 = $28, so I would owe my parents $28.
⦁ Think about how much time it will take you to create your product. You have 200 hours this summer to devote to creating your product. Write an inequality that represents your time constraint. Example: if each cup takes me 8 minutes to make, 8c ≤ 12,000 (since I’m working with minutes, I want to turn the 200 hours into minutes. 200 x 60 = 12000 minutes in 200 hours).
⦁ Solve your inequality from part D and graph your solution on a number line. Explain what your solution means in terms of the situation. Example: 8c ≤ 12,000, so c ≤ 1500minutes c ≤ 25 hours, so I am only using 1/8 of the 200 hours to make my product (to find out how many hours from minutes, divide the number of minutes by 60).
Task 1:
- The total amount of money I am willing to invest in this business is $50.
- I am going to make and sell handmade bracelets.
- My business will work by creating various styles of bracelets and selling them online and at local craft fairs.
- It will cost me $2.50 to make each bracelet.
- I will sell each bracelet for $10.
- I think my business will be profitable because the cost to make each bracelet is significantly lower than the selling price, resulting in a decent profit margin.
Task 2:
- Inequality: 2.50c ≤ 50 (where c represents the number of bracelets)
- Solution: I can only make a maximum of 20 bracelets with my $50 investment.
- The solution means that I cannot make more than 20 bracelets due to my spending limit.
- Equation: Total earnings = 10c - 2.50c
- With the given spending limit and selling price, the most money I can hope to earn is $150 (when selling all 20 bracelets).
- Total profit: $150 - $50 (initial investment) = $100. I made a profit of $100.
Task 3:
- Revised inequality: 2.50c ≤ 500 (since I now have an additional $300, making the new spending limit $500).
- Solution: c ≤ 200, meaning I can make a maximum of 200 bracelets.
- Total earnings with the new spending limit: 10(200) - 2.50(200) = $1750.
- I will have to pay my parents if I make more than $600.
- If I make $1750, I owe my parents 10% of $1150 (1750 - 600) which is $115.
- In terms of time constraint, the inequality would be 2.50c ≤ 12,000 (since it takes me 2.5 hours to make each bracelet and I have 200 hours).
- Solution: c ≤ 4,800 minutes or c ≤ 80 hours. This means that I will only use 1/2.5 of the 200 hours to make my product (to find out how many hours from minutes, divide the number of minutes by 60).