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.
a. What is the total amount of money you are willing to invest in this business?
b. What item are you going to make and sell? Why?
c. Describe how your business will work. How much will it cost you to make each item? How much will you sell each item for?
d. 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.
a. Write an inequality that represents the fact that while making your product you can't exceed this spending limit.
b. Solve this inequality and graph the solution on a number line. Explain what your solution means in terms of the situation.
c. 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.
d. 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?
e. 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? Now that you have these values, would you adjust your business plan from Task 1? If so, how?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.
a. Now that you have an additional $300, revise your inequality from part A of Task 2 to reflect your new spending limit. Solve this inequality and graph the solution on a number line. Explain what your solution means in terms of the situation.
b. If you still sell your item for the same price, what is the most money you can hope to earn from your business now?
c. Will you have to pay your parents? If so, determine how much you will owe them.
d. 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.
e. Solve your inequality from part D and graph your solution on a number line.
Explain what your solution means in terms of the situation.
f. With the costs taken into account, what was your total profit? Did you make or lose money? Now that you have these values, would you adjust your business plan from Task 1? If so, how? Make sure they all make sense and connect to each other
a. The total amount of money I am willing to invest in this business is $500.
b. I am going to make and sell handmade jewelry. I chose this item because it allows for creativity, requires low startup costs, and has a potential for high profit margins.
c. My business will work by purchasing jewelry-making supplies such as beads, wires, and clasps. Each item will cost me approximately $2 to make. I will sell each item for $10, allowing for a profit of $8 per item.
d. Yes, I believe my business will be profitable. With each item selling for $10 and a profit of $8 per item, I will be able to cover my costs and make a significant profit.
Task 2
a. The inequality that represents the spending limit is: 2x ≤ 500, where x represents the number of items made.
b. Solving the inequality:
2x ≤ 500
x ≤ 250
Graphing the solution on a number line:
[0, 250]
This solution means that I cannot make more than 250 items with the given spending limit of $500.
c. The equation representing total earnings is: Earnings = Price of item * Number of items sold.
d. Based on the solution from part b, the maximum number of items I can hope to sell is 250. Therefore, the most money I can hope to earn is $10 * 250 = $2500.
e. Taking into account the costs of $2 per item, the total profit is calculated as follows:
Total profit = (Price of item - Cost of item) * Number of items sold
Total profit = ($10 - $2) * 250 = $2000
I made a profit of $2000. Based on these values, I would not adjust my business plan as it is already profitable.
Task 3
a. After receiving an additional $300 from my parents, the revised spending limit can be represented by the inequality: 2x ≤ 800, where x represents the number of items made.
Solving the inequality:
2x ≤ 800
x ≤ 400
Graphing the solution on a number line:
[0, 400]
This solution means that I cannot make more than 400 items with the new spending limit of $800.
b. If I still sell each item for $10, the most money I can hope to earn is $10 * 400 = $4000.
c. Yes, I will have to pay my parents if I make more than $600. The amount I will owe them is 10% of the earnings above $600. Let's calculate this:
Earnings above $600 = Total earnings - $600
Earnings above $600 = $4000 - $600 = $3400
Amount owed to parents = 10% of earnings above $600 = 10% * $3400 = $340
d. The inequality representing the time constraint is: Time ≤ 200, where time is measured in hours.
e. Solving the inequality:
Time ≤ 200
This means that I cannot spend more than 200 hours creating my product.
Graphing the solution on a number line:
[0, 200]
This solution means that I have a maximum of 200 hours to create my product.
f. With the costs taken into account, the total profit can be calculated as follows:
Total profit = (Price of item - Cost of item) * Number of items sold
Total profit = ($10 - $2) * 400 = $3200
I made a profit of $3200. Based on these values, I would not adjust my business plan from Task 1 as it is still profitable.