To find the maximum total profit, we need to determine the maximum number of cakes that can be made within 200 hours.
Since it takes 3 hours to make one cake, the maximum number of cakes that can be made is 200 hours divided by 3 hours per cake, which is 66.67 cakes. We can round this down to 66 cakes because we cannot make a fraction of a cake.
The maximum total cost of making 66 cakes is 66 cakes multiplied by $14, which is $924.
The maximum total revenue from selling 66 cakes is 66 cakes multiplied by $50, which is $3300.
Therefore, the maximum total profit is $3300 - $924 = $<<3300-924=2376>>2376. Answer: \boxed{2376}.
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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?
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