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.
≥ < > ≤
*
1 point
b)
Solve this inequality and choose the graph of the solution.
* Make sure to round to the nearest dollar.
Do not include dollar signs in the solution
You can copy and paste the inequality sign below in your answer.
≥ < > ≤
***Make sure to have x and an inequality sign in your answer
*
1 point
Choose the graph of the solution to part b above.
1 point
Captionless Image
Option A
Option B
Option C
Option D
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
*
1 point
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?
*
1 point
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?
*
1 point
Did you make money or lose money?
*
1 point
Make Money
Lose Money
a) The inequality that represents the cost of making x amount of cakes should not exceed the investment is:
14x ≤ 10000
b) Solving the inequality:
14x ≤ 10000
x ≤ 10000/14
x ≤ 714.29 (rounded to the nearest whole number)
Therefore, x ≤ 714.
The graph would be a vertical line at x = 714.
c) The equation that represents the total earnings, T, based on the price of the cake and how many you sell is:
T = 50x
d) The most money you can hope to earn from your business is when you sell all the cakes, so x = 714.
T = 50*714
T = $35,700
Therefore, the most money you can hope to earn is $35,700.
e) To calculate the total profit, we need to subtract the total cost from the total earnings. The total cost is $14 per cake multiplied by the number of cakes:
Total cost = 14*714 = $9,996
Total profit = Total earnings - Total cost = $35,700 - $9,996 = $25,704
Since the total profit is positive, you made money.