In Task 1 you determined how much of your own money you’re willing to spend to

Question

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?

Answer 1

a. The inequality that represents the fact that while making your product you can't exceed the spending limit is:
Total spending on the product ≤ Spending limit

b. Let's assume the spending limit is $500. The inequality becomes:
Total spending on the product ≤ $500

To solve the inequality, we need more information about the specific costs involved in making the product. Let's say the cost per item is $10 and you plan to make x number of items. The total spending on the product can be represented as:
Total spending = Cost per item * Number of items
Total spending = $10 * x

The inequality becomes:
$10 * x ≤ $500

To solve this inequality, divide both sides by $10:
x ≤ $500 / $10
x ≤ 50

The solution x ≤ 50 means that you can make a maximum of 50 items without exceeding your spending limit.

c. The equation that represents your total earnings based on the price of your item and how many you sell is:
Total earnings = Price per item * Number of items sold

Let's assume the price per item is $20 and you sell y number of items. The equation can be represented as:
Total earnings = $20 * y

d. Using the answer from part B, we know that the maximum number of items you can make is 50. Using the equation from part C, the maximum earnings you can hope to earn from your business is:
Total earnings = $20 * 50
Total earnings = $1000

Therefore, the most money you can hope to earn from your business is $1000.

e. The total profit can be calculated by subtracting the total spending from the total earnings:
Total profit = Total earnings - Total spending

Let's assume you made a total spending of $400 (including the cost of making 50 items). Using the equation from part C, the total earnings are $1000.

Therefore, the total profit = $1000 - $400 = $600

You made a profit of $600.

Based on these values, since you made a profit, there may not be a need to adjust your business plan from Task 1. However, it would depend on other factors such as market demand, competition, and feasibility of production.