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.
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.
b) x ≤ 714r
c) T = 50x
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?
is $357,000,000
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 total cost from the total earnings.
Total cost = $14/cake * x cakes
Total earnings = $50/cake * x cakes
Total profit = Total earnings - Total cost
Given that x ≤ 714r, we can substitute the value of x into the equation:
Total profit = $50/cake * (714r) - $14/cake * (714r)
Total profit = $35700r - $9996r
Total profit = $25704r
Since we don't have the value of r, we can't calculate the exact total profit.
To calculate the total profit, we first need to determine the number of cakes you can make with the initial investment of $10,000.
Since it costs $14 to make each cake and you want to earn maximum profit, we can use the inequality from part b: x ≤ 714r.
Plug in the given information:
x ≤ 714r
x ≤ 714(10,000/14)
x ≤ 714(714.29)
x ≤ 510,000
Now, we know that the maximum number of cakes you can make is 510,000.
To find the total profit, we need to subtract the total cost from the total revenue.
Total cost = Cost per cake × Number of cakes = $14 × 510,000 = $7,140,000
Total revenue = Revenue per cake × Number of cakes = $50 × 510,000 = $25,500,000
Total profit = Total revenue - Total cost = $25,500,000 - $7,140,000 = $18,360,000
Therefore, the total profit from your business, taking into account the initial investment and costs, is $18,360,000.
To find the most money you can hope to earn from your business, we need to use the equation from part c, which is T = 50x. Here, T represents the total income earned from selling cakes, and x represents the number of cakes sold.
Based on the information provided, it costs you $14 to make each cake, so let's assume you sell each cake for a price higher than this cost to make a profit.
Considering this, let's calculate the maximum number of cakes you can sell given the $10,000 total investment:
Total Investment = Total Cost of Cakes
$10,000 = $14 (cost per cake) * x (number of cakes)
Simplifying the equation:
$10,000 = 14x
Now, divide both sides of the equation by 14 to isolate x:
x = $10,000 / 14
x ≈ 714.29
Since you cannot sell a fraction of a cake, the maximum number of cakes you can sell is 714.
Now, substitute the value of x into the equation T = 50x to calculate the total income:
T = 50 * 714
T = $35,700
Therefore, the most money you can hope to earn from your business is $35,700 (selling 714 cakes).
Moving on to part e,
To calculate the total profit, you need to subtract the total cost of making cakes from the total income earned.
Total cost of making cakes = cost per cake * number of cakes = $14 * 714 cakes = $9,996
Total profit = Total income earned - Total cost of making cakes
Total profit = $35,700 - $9,996
Total profit = $25,704
So, considering the costs taken into account, your total profit is $25,704.