f)
Now that you have an additional $300, revise your inequality from part a to reflect your new spending limit. Solve this inequality.
* Do not include the dollar symbol in the inequality
You can copy and paste the inequality sign below in your answer.
≥ < > ≤
x ≤ 700
To revise the inequality from part a to reflect the new spending limit, you would first need to determine the original inequality from part a. Since the specific inequality from part a is not mentioned, I won't be able to provide you with the revised inequality.
However, I can guide you on how to revise it yourself. Here are the steps:
1. Identify the original inequality from part a. Let's say it was something like "x ≤ 500" (spending limit was $500).
2. To reflect the additional $300, add $300 to both sides of the inequality. The revised inequality will be "x + 300 ≤ 800".
3. Remove any dollar symbols from the inequality.
After revising the inequality, you should be able to solve it properly to find the new spending limit. Make sure to provide the original inequality from part a to get a specific solution for your problem.
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.
If so, determine how much you will owe your parents.
To determine how much you will owe your parents, we need to compare your additional profit to the threshold of $600.
Let's denote your additional profit as x.
If x is greater than $600, you will owe your parents 10% of the amount exceeding $600.
Therefore, the amount you will owe your parents can be calculated using the following equation:
Amount owed = 10% * (x - 600)
For example, if your additional profit is $650, we substitute x = 650 into the equation:
Amount owed = 10% * (650 - 600) = 10% * 50 = $5
So, if you earn $650, you would owe your parents $5.
Note: If your additional profit is equal to or less than $600, then you do not owe your parents anything.
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?
To find the maximum total profit, we need to consider the cost of making the cakes and the revenue from selling them.
The cost of making each cake is $14, and the selling price is $50.
Let's denote the number of cakes made as c.
The total cost of making the cakes is given by:
Total cost = Cost per cake * Number of cakes
Total cost = 14c
The total revenue from selling the cakes is given by:
Total revenue = Selling price per cake * Number of cakes
Total revenue = 50c
The profit can be calculated by subtracting the total cost from the total revenue:
Profit = Total revenue - Total cost
Profit = 50c - 14c
Profit = 36c
To find the maximum profit, we need to determine the maximum value of c, which is the number of cakes made. However, the maximum number of hours spent making the cakes is given as 200.
Let's denote the number of hours spent making each cake as h.
The total time spent making the cakes is given by:
Total time = Time per cake * Number of cakes
Total time = h * c
We know that the total time spent making the cakes is 200 hours:
Total time = 200
Substituting the equation for total time into the equation for number of cakes:
200 = h * c
Solving for c:
c = 200 / h
Now we can substitute this value of c into the equation for profit:
Profit = 36c
Profit = 36 * (200 / h)
To find the maximum profit, we need to find the value of h that minimizes the denominator.
Since the cost per cake is $14 and the selling price per cake is $50, the profit per hour spent making the cakes is:
Profit per hour = (Profit per cake) / (Time per cake)
Profit per hour = (50 - 14) / h
Profit per hour = 36 / h
To maximize the profit, we need to maximize the profit per hour. This occurs when the time per cake is minimized. Therefore, the minimum value for h is the value that maximizes the profit.
As h approaches infinity, the profit per hour approaches 0. This means that the time spent making each cake approaches 0, resulting in an infinite number of cakes made and a maximum total profit.
Therefore, the maximum total profit is infinite.