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 calculate the maximum total profit, we need to know the number of cakes that can be made within 200 hours.

Let's assume it takes x hours to make one cake. Therefore, the equation for the number of cakes made within 200 hours is:
200 / x = number of cakes made

Since each cake costs $14 to make and is sold for $50, the profit per cake is $50 - $14 = $36.

Thus, the maximum total profit can be obtained by multiplying the number of cakes made by the profit per cake:
Profit = ($50 - $14) * (200 / x)

However, we need to find the maximum total profit. This can be achieved by finding the maximum number of cakes made within 200 hours. Let's analyze this situation:

If it takes 1 hour to make a cake, then the number of cakes made within 200 hours would be 200 / 1 = 200 cakes.
Profit = ($50 - $14) * (200 / 1) = $36 * 200 = $7200

If it takes 2 hours to make a cake, then the number of cakes made within 200 hours would be 200 / 2 = 100 cakes.
Profit = ($50 - $14) * (200 / 2) = $36 * 100 = $3600

If it takes 3 hours to make a cake, then the number of cakes made within 200 hours would be 200 / 3 ≈ 66.67 cakes.
Since we cannot make a fraction of a cake, the maximum number of cakes made within 200 hours would be 66.
Profit = ($50 - $14) * (200 / 3) = $36 * 66 = $2376

We can continue this analysis until we reach the maximum number of cakes made within 200 hours.

Therefore the maximum total profit would be $7200, achieved by making 200 cakes.