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.
≥ < > ≤
The inequality that represents the cost of making x amount of cakes should not exceed this investment is:
14x ≤ 10000
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
To solve the inequality 14x ≤ 10000, we divide both sides of the inequality by 14:
x ≤ 10000/14
To round this to the nearest whole number, we get:
x ≤ 714
The graph of the solution would be a closed dot on the number line at 714, and shading to the left, indicating that x is less than or equal to 714.
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?
From part b, we found that the maximum number of cakes you can make is 714 given the investment of $10,000.
Using the equation from part c (T = 50x), we can calculate the maximum amount of money you can hope to earn:
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 determine the total profit, we need to subtract the total cost from the total earnings.
The total cost is the cost per cake multiplied by the number of cakes made:
Total cost = 14 * 714
Total cost = $9,996
The total earnings can be calculated using the equation T = 50x, where x is the number of cakes sold.
Total earnings = 50 * 714
Total earnings = $35,700
Total profit = Total earnings - Total cost
Total profit = $35,700 - $9,996
Total profit = $25,704
Therefore, the total profit is $25,704.