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?
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.
a. The inequality that represents the fact that you cannot exceed your spending limit is:
Total spending on product ≤ Spending limit
b. To solve this inequality, we need to know the specific spending limit value. Let's assume the spending limit is $1000. The inequality becomes:
Total spending on product ≤ $1000
Now, let's graph the solution on a number line. Since the spending limit is a maximum value, we represent it with a closed circle on $1000 and shade to the left:
--------[==================]----------
Explanation: The solution on the number line indicates that the total spending on the product should be less than or equal to $1000. Any point to the left of the shaded area represents total spending that is within the limit.
c. The equation that represents your total earnings based on the price of your item and how many you sell can be expressed as:
Total Earnings = Price per item * Number of items sold
d. Using the solution from part (b) and the equation from part (c), we can determine the most money you can hope to earn from your business. If we assume the price per item is $10 and the number of items sold is 100, the calculation would be as follows:
Total Earnings = $10 * 100 = $1000
So, the most money you can hope to earn from your business, based on the given values, is $1000.
e. To calculate the total profit, we need to subtract the total spending on the product from the total earnings:
Total Profit = Total Earnings - Total spending on product
Let's assume the total spending on the product is $800. Using the values from part (d), we can calculate the total profit:
Total Profit = $1000 - $800 = $200
Since the total profit is positive $200, it means you made money from your business.
Based on these values, if the total profit meets your expectations and you are satisfied with the earnings, you may not need to adjust your business plan from Task 1. However, if the total profit is not satisfactory, you may consider modifying your business plan by increasing the price per item, finding ways to reduce costs, or exploring additional revenue streams.
a. The inequality that represents the fact that you can't exceed your spending limit can be written as:
Cost of making your product ≤ Spending limit
b. To solve this inequality and graph the solution on a number line, you need to first determine the spending limit value and then plot it on the number line.
For example, let's say your spending limit is $500. The inequality becomes:
Cost of making your product ≤ $500
On the number line, you would plot a closed circle at $500 to represent the spending limit. Then, you would shade the area to the left of the circle to indicate that the cost of making your product should be less than or equal to $500. This ensures you do not exceed your spending limit.
c. The equation that represents your total earnings based on the price of your item and how many you sell can be written as:
Total earnings = Price of item × Number of items sold
For example, if you sell each item for $10 and sell 50 items, the equation becomes:
Total earnings = $10 × 50
d. To determine the most money you can hope to earn from your business, you need additional information such as the price of your item and the number of items you expect to sell. Once you have those values, substitute them into the equation from part C and calculate the total earnings. The result will be the most money you can hope to earn from your business.
e. To determine your total profit, you need to take into account the costs of making your product and subtract that from your total earnings. If your total earnings are higher than the total costs, then you have made a profit. If your total earnings are lower than the total costs, then you have incurred a loss.
Total profit = Total earnings - Total costs
Based on the values you have for total earnings, total costs, and spending limit, you can calculate your total profit. If your total profit is positive, it means you made money. If it is negative, it means you lost money.
Considering these values, you can evaluate whether your business plan from Task 1 needs adjustment. If you have made a profit, you may consider continuing with the same plan. However, if you have incurred a loss, you might want to reassess your plan and make necessary adjustments such as reducing costs, increasing prices, or exploring new marketing strategies.