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?
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}.
To calculate the maximum total profit, we need to determine how many cakes can be made using the given 200 hours of time and then calculate the profit for each cake.
To find out how many cakes can be made, we need to know how much time it takes to make one cake. Let's assume it takes x hours to make one cake. Since we have 200 hours in total, the number of cakes that can be made is 200 divided by x.
The cost to make one cake is given as $14, and the selling price of each cake is $50. Therefore, the profit made from selling one cake is the selling price minus the cost to make one cake, which is $50 - $14 = $36.
Now, let's calculate the maximum profit. We can do this by multiplying the profit per cake by the number of cakes that can be made with the given time.
Maximum profit = (Profit per cake) x (Number of cakes)
Number of cakes = 200 / x
Maximum profit = $36 x (200 / x)
To find the maximum profit, we need to determine the value of x, which is the number of hours it takes to make one cake. Unfortunately, the given information doesn't provide us with enough details to determine this value.
Therefore, without knowing the number of hours it takes to make one cake, we cannot calculate the maximum total profit.
To calculate the maximum total profit, we need to consider the costs incurred and the revenue generated.
1. Calculate the total cost:
The cost to make each cake is $14, and if we spend 200 hours making the cakes, the total cost would be 14 * 200 = $2,800.
2. Calculate the revenue generated:
The selling price for each cake is $50, and since we made the cakes in 200 hours, we can calculate the number of cakes made by dividing 200 by the time it takes to make one cake.
Let's assume it takes 1 hour to make one cake. Therefore, the number of cakes made is 200 / 1 = 200.
The revenue generated would be 50 * 200 = $10,000.
3. Calculate the maximum total profit:
The maximum total profit can be calculated by subtracting the total cost from the revenue generated.
Profit = Revenue - Cost = $10,000 - $2,800 = $7,200.
Therefore, the maximum total profit would be $7,200.