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.