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,
what changes would you make? If not, explain why not.
a. The inequality that represents the fact that while making your product you can't exceed this spending limit is:
Cost of making the product ≤ Spending limit
b. To solve the inequality and graph the solution on a number line, we need to know the specific values for the spending limit and the cost of making the product. Additionally, we need to assume the cost of making the product is a continuous variable.
c. The equation that represents total earnings based on the price of the item and how many you sell is:
Total Earnings = Price per Item × Number of Items Sold
d. To find the most money you can hope to earn from your business, you would need to know the specific values for the price per item and the number of items sold. Without these values, it is not possible to provide a specific answer.
e. To calculate the total profit, you need to subtract the total costs from the total earnings. If the total profit is positive, it means you made money, and if it is negative, it means you incurred a loss. Without the specific values for total costs and total earnings, it is not possible to determine if you made money or lost money. Based on the given information, it is not possible to determine if adjustments to the business plan are necessary without additional details.
a. To represent the fact that your spending on the product cannot exceed your spending limit, you can write the inequality as:
Product spending ≤ Spending Limit.
b. To solve this inequality and graph the solution on a number line, you need to have specific values for the spending limit. Let's say your spending limit is $500. The inequality can then be written as:
Product spending ≤ $500.
To graph this solution on a number line, draw a line and label one endpoint as $500 (since spending cannot exceed this amount). Then shade the region to the left of $500 to represent all the possible spending values within the limit.
c. To write an equation that represents your total earnings based on the price of your item (let's call it 'p') and the number of items sold (let's call it 'n'), you can write:
Total Earnings = Price per item × Number of items sold.
If you determined in Task 1 that the price per item is $x and the number of items sold is 'n', the equation would be:
Total Earnings = x × n.
d. To determine the most money you can hope to earn from your business, you need to know the specific values of 'x' (price per item) and 'n' (number of items sold). Without those values, we cannot calculate the potential earnings.
e. To calculate your total profit, you would need to subtract your total spending from your total earnings. However, without knowing the values for spending and earnings, it is not possible to determine if you made money or lost money.
Based on the information provided, we cannot adjust the business plan from Task 1 as we do not have the necessary values to make informed decisions.