To find the most money you can hope to earn from your business, we need to use the equation you provided in part c: T = 50x, where T represents the total money you can earn and x represents the number of cakes sold.
Since the equation T = 50x represents the total money earned from selling cakes, we need to substitute x with the maximum number of cakes you can sell.
To find the maximum number of cakes you can sell, we will consider the equation from part b: x ≤ 714r, where x represents the number of cakes sold and r represents the amount of money you invested.
Given that you invested $10,000, we can substitute r with 10,000:
x ≤ 714(10,000)
Simplifying this equation, we get:
x ≤ 7,140,000
So, the maximum number of cakes you can sell is 7,140,000.
Now we can substitute this value of x into the equation T = 50x to find the most money you can hope to earn:
T = 50(7,140,000)
T = 357,000,000
Therefore, the most money you can hope to earn from your business is $357,000,000.
Now, to calculate the total profit, we need to subtract the cost of making the cakes from the total money earned:
Total profit = Total money earned - Total cost
The total cost is calculated by multiplying the cost per cake ($14) by the number of cakes sold (x).
Total cost = 14x
Total cost = 14(7,140,000)
Total cost = 99,960,000
Total profit = 357,000,000 - 99,960,000
Total profit = $257,040,000
Therefore, your total profit, taking into account the investment and the cost of making the cakes, is $257,040,000.