Task 2
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.
Write an inequality that represents the fact that while making your product you can’t exceed this spending limit. (If I invested $200 to start, the cost per item is less than or equal the total money you have to invest, for example if the cups of lemonade cost $.63 per cup: .63c ≤ 200 [.63 cents per cup is less than or equal to $200])
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Solve this inequality. Example: .63c ≤ 200 or c ≤ 317.4, so I can only make 317 cups with my $200 (317 instead of 317.4 because you can’t make .4 cups)
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Explain what your solution means in terms of the situation. Example: so I can only make 317 cups with my $200 (317 instead of 317.4 because you can’t make .4 cups)
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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. Example: If I charge $1.50 per cup, and it costs .63 per cup to make - 1.50c - .63c = total earnings. If I sell 50 cups: 1.50(50) - .63(50) = 43.50.
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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? SHOW THE EQUATION Example: What will be your total profit based on how many items you can sell, depending on what you invest: 1.50(317) - .63(317) = 275.79
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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? If so, how? Example: I only invested $8 to start, so $275.79 - $8 = 276.79, so I made a profit of $276.79.
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The inequality representing the spending limit is:
Cost per item ≤ Total money invested
The solution to this inequality is:
c ≤ Total money invested / Cost per item
This means that the maximum number of items that can be made is equal to the total money invested divided by the cost per item. However, since the number of items must be a whole number, we would round the result down to the nearest whole number.
The equation representing the total earnings is:
Total earnings = Price per item * Number of items sold - Cost per item * Number of items sold
Using the answer from part B and the equation from part C, the most money that can be earned from the business is:
Total earnings = (Price per item * (Total money invested / Cost per item) - Cost per item * (Total money invested / Cost per item)
To calculate the total profit, we need to subtract the total money invested from the total earnings. If the result is positive, it means a profit was made. If the result is negative, it means a loss was incurred.