You want to start a bakery business to earn money. The total amount of money you will invest is $10,000. You will be selling cakes. It will cost you $14 to make each cake.
a)
Write an inequality that represents the cost of making x amount of cakes should not exceed this investment.
* Do not include the dollar symbol in the inequality
You can copy and paste the inequality sign below in your answer.
≥ < > ≤
b)
Solve this inequality and choose the graph of the solution.
* Make sure to round to the nearest whole number.
Do not include dollar signs in the solution
a) The inequality that represents the cost of making x amount of cakes should not exceed the investment of $10,000 is:
14x ≤ 10000
b) To solve this inequality, divide both sides by 14:
x ≤ 10000/14
x ≤ 714.29
Rounded to the nearest whole number, the solution is x ≤ 714.
The graph of the solution would be a closed dot on 714 on the number line, indicating that 714 or any value less than 714 is a valid solution.
c)
You plan to sell each cake for $50. Write an equation that represents your total earnings, T, based on the price of your cake and how many you sell. Let x represent the number of cakes you sell.
* Use T and x as your variables
The equation that represents your total earnings, T, based on the price of your cake and how many you sell is:
T = 50x
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?
Based on the answer from part b, we know that the maximum number of cakes you can sell is 714.
Using the equation from part c, where T represents your total earnings and x represents the number of cakes you sell, we have:
T = 50x
Substituting x = 714 into the equation:
T = 50 * 714
T = 35,700
Therefore, the most money you can hope to earn from your business is $35,700.
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?
To calculate the total profit, we need to subtract the cost of making the cakes from the total earnings.
The cost of making each cake is $14, and we know from part b that the maximum number of cakes you can sell is 714.
The total cost of making the cakes is 14 * 714 = $9,996.
The total earnings, as calculated in part d, is $35,700.
Therefore, the total profit can be calculated as:
Total profit = Total earnings - Total cost of making the cakes
Total profit = $35,700 - $9,996
Total profit = $25,704
So, the total profit from your business, taking into account the costs, is $25,704.