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.
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?
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?
a. To determine the total amount of money you are willing to invest in this business, you need to consider your budget and how much you can afford to spend. Let's say you have determined that you can invest up to $500.
b. The item you choose to make and sell should be reasonable within your budget and have a potential market demand. For example, you could consider making and selling homemade jewelry or crafts, where the cost of materials is relatively low and there is potential for profit.
c. Your business will work by creating and selling your chosen item. You need to calculate the cost of making each item, including the cost of materials. Let's say the cost to make each item is $5. You will also need to decide on the selling price for each item. Let's assume you will sell each item for $15.
d. To determine if your business will be profitable, you need to compare your expenses (cost to make each item) with your revenue (selling price per item). In this case, your profit per item would be $15 (selling price) - $5 (cost to make) = $10. If you can sell enough items to cover your expenses and make a profit, then your business has the potential to be profitable.
Task 2:
a. The inequality that represents your spending limit while making your product would be: cost to make each item * number of items ≤ total amount of money you are willing to invest. In this case, it would be 5x ≤ 500, where x represents the number of items.
b. To solve the inequality, divide both sides by 5: x ≤ 100. This means that you cannot make more than 100 items with your available budget. On a number line, you would represent this by shading everything to the left of 100, as it represents the number of items you can afford.
c. The equation that represents your total earnings based on the price of your item and how many you sell is: total earnings = selling price per item * number of items sold. In this case, it would be total earnings = 15x.
d. Using the solution from part b (x ≤ 100) and the equation from part c (total earnings = 15x), the most money you can hope to earn from your business is 15 * 100 = $1500.
e. Taking the costs into account, your total profit would be the total earnings minus the total expenses. Let's assume you made and sold 80 items. Your total earnings would be 15 * 80 = $1200. The total expenses would be the cost to make each item * number of items, which is 5 * 80 = $400. Therefore, your total profit would be $1200 - $400 = $800. In this case, you made money.
Considering the values obtained, you might consider adjusting your business plan from Task 1. For example, if you have a high demand for your product and are able to sell more items, you could increase your production to maximize your profit.
Task 3:
a. With an additional $300 from your parents, the revised inequality would be: cost to make each item * number of items ≤ total amount of money you are willing to invest + $300. In this case, it would be 5x ≤ $500 + $300.
b. By solving the new inequality, you would get: x ≤ 160. This means you can make and sell up to 160 items with the additional $300. On a number line, you would represent this by shading everything to the left of 160.
c. If you still sell your item for the same price, the most money you can hope to earn from your business now would be 15 * 160 = $2400.
d. According to the condition set by your parents, if you make more than $600 total, you have to give them 10% of your earnings above $600. Let's assume you earned $2400. The amount above $600 would be $2400 - $600 = $1800. 10% of $1800 is $180. Therefore, you would owe your parents $180.
e. The inequality representing your time constraint is: time to make each item * number of items ≤ total available time. In this case, it would be 200x ≤ 200 (total available time).
f. By solving the inequality, you would get: x ≤ 1. This means you can make and sell up to 1 item within the given time constraint. On a number line, you would represent this by shading everything to the left of 1.
Considering the values obtained, your total profit would depend on the number of items you are able to make and sell within the given time constraint. If you can sell the maximum 1 item, your total earnings would be $15. However, you would need to deduct the cost to make the item ($5) and the amount owed to your parents ($180) from that earnings. In this case, you would have a negative profit of -$170. Therefore, with these values, you would need to adjust your business plan from Task 1, considering the time constraints and potential loss.