Your parents heard about the success of your business and they want to help you out. Suppose they want to give you an additional $300 to put toward your business. However, there’s a catch. If you make more than $600 additional profit, you have to give them 10% of your earnings above $600. For example, if you have earned $650, then you owe 10% of $50, or $5, to your parents.
k)
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?
*
1 point
If it costs $14 to make each cake and you are selling them for $50 each, your profit per cake is $50 - $14 = $36.
Since you spent 200 hours making the cakes, you are able to make a total of 200 / 3 = 66.67 cakes (rounded to the nearest whole number).
Since you can't make a fraction of a cake, the maximum number of cakes you can make is 66.
Therefore, your maximum total profit is 66 * $36 = $2376.
To calculate your maximum total profit, you need to consider the cost of making the cakes, the number of cakes you can produce in 200 hours, and the selling price of each cake.
Given:
Cost to make each cake = $14
Selling price of each cake = $50
Total time spent making cakes = 200 hours
1. First, calculate the number of cakes you can produce in 200 hours:
Number of cakes = Total time spent making cakes / Time required to make one cake in hours
Number of cakes = 200 hours / Time required to make one cake in hours
2. Calculate the profit per cake:
Profit per cake = Selling price of each cake - Cost to make each cake
3. Calculate the maximum total profit:
Maximum total profit = Number of cakes * Profit per cake
Follow these steps to find your maximum total profit.
To calculate your maximum total profit, we need to consider the cost of making the cakes and the selling price.
Given that it costs $14 to make each cake and you are selling them for $50 each, the profit per cake can be calculated as:
Profit per cake = Selling price - Cost price
= $50 - $14
= $36
Now, to find the maximum total profit, we need to calculate the maximum number of cakes you can make within the 200 hours. To do this, we need to divide the total number of hours by the time it takes to make one cake.
Let's assume it takes x hours to make one cake. Since you can make 200/x cakes in 200 hours, the total profit can be calculated as:
Total profit = Profit per cake * Number of cakes
= $36 * (200/x)
To maximize the profit, we need to find the number of cakes that will maximize the total profit. We can do this by finding the derivative of the total profit with respect to the number of cakes (200/x), and setting it equal to zero:
d(Total profit) / d(200/x) = 0
Let's calculate the derivative:
d(Total profit) / d(200/x) = 36 - 36 * (200/x^2)
Setting it equal to zero and solving for x, we get:
36 - 36 * (200/x^2) = 0
(200/x^2) = 1
x^2 = 200
x = sqrt(200)
x ≈ 14.14
Since it's not possible to make 0.14 of a cake, we can round down to 14 cakes.
Therefore, the maximum total profit you can make by spending 200 hours making cakes is:
Total profit = Profit per cake * Number of cakes
= $36 * 14
= $504