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.
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.
≥ < > ≤
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
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?
Let's solve the inequality for the number of cakes you need to sell to make a profit:
Profit = Total Earnings - Total Cost
Total Cost = Cost per cake * Number of cakes
Total Earnings = Price per cake * Number of cakes
Profit = (Price per cake * Number of cakes) - (Cost per cake * Number of cakes)
Profit = (50 * x) - (14 * x)
Now, we can determine the most money you can hope to earn from your business by finding the maximum possible value of the profit. This occurs when the number of cakes sold, x, is maximized. Since there is no further information provided, we can assume that x can take any positive real value.
Therefore, the most money you can hope to earn from your business is infinite.
Next, let's calculate the total profit. Total profit is the profit minus the initial investment.
Total Profit = Profit - Initial Investment
Total Profit = ((50 * x) - (14 * x)) - 10000
Please note that I used $10,000 as the Initial Investment, assuming that it is the full investment amount mentioned at the beginning of the question.
Total Profit = 36 * x - 10000
To solve the inequality and choose the graph of the solution, we need to calculate the maximum number of cakes we can make with the given investment.
Let's set up the inequality:
Total Investment ≥ Cost per Cake * Number of Cakes
$10,000 ≥ $14 * x
To find the maximum value of x (number of cakes), we can divide both sides of the inequality by $14:
$10,000 / $14 ≥ x
714.29 ≥ x
Rounding to the nearest dollar, we get:
715 ≥ x
So, the maximum number of cakes we can make is 715.
Now, let's move on to part c.
The equation that represents the total earnings, T, based on the price of each cake and the number of cakes sold can be written as:
T = Price per Cake * Number of Cakes
T = $50 * x
Now, let's find the most money we can hope to earn from the business using the equation from part c and the maximum number of cakes from part d:
T = $50 * 715
T = $35,750
So, the most money we can hope to earn from the business is $35,750.
Finally, to calculate the total profit, we need to subtract the total investment from the total earnings:
Total Profit = Total Earnings - Total Investment
Total Profit = $35,750 - $10,000
Total Profit = $25,750
Therefore, the total profit is $25,750.
To solve this problem, we need to follow these steps:
a) Write and solve an inequality to determine the number of cakes that need to be sold to not lose money:
We know that it costs $14 to make each cake and we are willing to invest $10,000. Therefore, the number of cakes that need to be sold to not lose money can be found by:
14x ≤ 10,000, where x represents the number of cakes sold.
Now, we can solve it for x.
Dividing both sides of the inequality by 14 gives us:
x ≤ 10,000 / 14
Calculating this result will give us the rounded answer for the maximum number of cakes that need to be sold.
b) Write an equation to represent the total earnings based on the price of the cake and the number of cakes sold:
We know that the selling price per cake is $50. Therefore, the equation representing the total earnings, T, based on the number of cakes sold, x, would be:
T = 50x
c) What is the most money you can hope to earn from your business?
To find the maximum amount of money that can be earned, we need to substitute the value we found in part a into the equation from part b.
T = 50 * (10,000 / 14)
Calculating this equation will give us the rounded answer for the maximum earnings.
d) To find the total profit, we need to subtract the total cost (initial investment) from the total earnings:
Total Profit = Total Earnings - Initial Investment
Calculating this will give us the rounded answer for the total profit.