Remember it costs $14 to make the cakes and you are selling them for $50 each. If you only spend the 200 hours making the cakes, what was your maximum total profit?

Answer 1

To find the maximum total profit, we need to determine the maximum number of cakes we can make within the 200 hours and multiply it by the profit per cake.

Since it costs $14 to make each cake and we are selling them for $50 each, the profit per cake is $50 - $14 = $36.

Let's assume it takes x hours to make one cake.
To find the maximum number of cakes we can make in 200 hours, we divide 200 by x.
So, the maximum number of cakes we can make is 200 / x.

To maximize the profit, we need to maximize the number of cakes, which means we need to minimize the time it takes to make one cake.

Therefore, we need to find the minimum value of x that still satisfies the condition 200 / x = an integer.

The factors of 200 are 1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100, 200.
We need to find the largest factor of 200 that is smaller or equal to 200 hours.
We see that the largest factor is 50.

Therefore, it takes 50 hours to make one cake.
The maximum number of cakes we can make in 200 hours is 200 / 50 = 4 cakes.

The maximum total profit is 4 cakes * $36 per cake = $144. Answer: \boxed{144}.