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 calculate the maximum total profit, we need to multiply the profit per cake by the number of cakes produced and sold. The profit per cake is the selling price minus the cost to make each cake.
First, let's find the profit per cake:
Profit per cake = Selling price - Cost to make each cake
Therefore, profit per cake = $50 - $14 = $36
Next, we need to determine the number of cakes produced and sold. To do this, we divide the total hours spent making the cakes by the time it takes to make each cake.
Number of cakes = Total hours / Time to make each cake
Therefore, number of cakes = 200 hours / Time to make each cake
However, we don't know the time it takes to make each cake. If you provide that information, we can proceed with the calculation.
To calculate the maximum total profit, we need to determine the number of cakes that can be made in 200 hours.
Let's assume it takes x hours to make one cake.
Therefore, the equation will be:
x * y = 200,
where y represents the number of cakes that can be made.
To find the maximum number of cakes, we want to minimize x.
So, let's assume it takes the minimum amount of time to make one cake, which is 2 hours.
Plugging this into the equation, we have:
2 * y = 200.
Simplifying this equation, we get:
y = 200 / 2 = 100.
So, the maximum number of cakes that can be made in 200 hours is 100.
Now, let's calculate the maximum total profit:
Profit per cake = Selling price - Cost price
= $50 - $14
= $36.
Maximum total profit = Profit per cake * Number of cakes
= $36 * 100
= $3600.
Therefore, the maximum total profit you can make by selling 100 cakes in 200 hours is $3600.
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.