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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?
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}.
To calculate the maximum total profit, we need to consider the cost of making the cakes and the revenue generated from selling them.
1. Calculate the total cost: Since it costs $14 to make each cake, we multiply the cost per cake by the number of cakes we can make in the given 200 hours. Assuming each cake takes 1 hour to make, we can make a total of 200 cakes.
Total cost = $14 x 200 cakes = $2800
2. Calculate the total revenue: Since each cake is sold for $50, we multiply the selling price per cake by the number of cakes sold.
Total revenue = $50 x 200 cakes = $10,000
3. Calculate the maximum total profit: Subtract the total cost from the total revenue.
Maximum total profit = Total revenue - Total cost
= $10,000 - $2800
= $7200
Therefore, the maximum total profit you can make is $7200.
To calculate the maximum total profit, we need to consider both the cost of making the cakes and the revenue from selling them. The profit can be calculated by subtracting the cost from the revenue.
First, let's calculate the revenue:
The selling price of each cake is $50.
If you sell all the cakes, the total revenue can be calculated by multiplying the selling price per cake ($50) by the number of cakes produced. To find the number of cakes produced, we need to divide the total number of hours spent making cakes (200) by the time it takes to make one cake.
To find the time it takes to make one cake, we need to divide the total time spent making cakes (200 hours) by the number of cakes produced.
Let's assume it takes "x" hours to make one cake. Therefore, the equation becomes:
x * number of cakes = total time spent (200 hours)
x = 200 / number of cakes
Now, let's calculate the cost:
The cost of making each cake is $14.
So, the total cost can be calculated by multiplying the cost per cake ($14) by the number of cakes produced.
Finally, let's calculate the profit:
The profit is calculated by subtracting the cost from the revenue.
Profit = Revenue - Cost
To find the maximum total profit, we can iterate through different numbers of cakes produced to find the maximum profit. We start with producing one cake and increment the number of cakes until we reach a point where the profit starts decreasing.
By comparing the profits obtained from different quantities of cakes, we can determine the maximum total profit.