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.
f)
Now that you have an additional $300, revise your inequality from part a to reflect your new spending limit. Solve this inequality. Make sure to round to the nearest dollar.
* Do not include the dollar symbol in the inequality
You can copy and paste the inequality sign below in your answer.
≥ < > ≤
*Make sure to solve the inequality and write x and an inequality sign in your answer.
*
1 point
Choose the graph of the solution to part f above
*
1 point
Captionless Image
Option A
Option B
Option C
Option D
Other:
g)
If you still sell your item for the same price, what is the most money you can hope to earn from your business now?
*
1 point
h)
Will you have to pay your parents?
*
1 point
Yes
No
If so, determine how much you will owe your parents.
*
1 point
i)
You are trying to decide if it is worth the investment to make the cakes if it takes 2.5 hours to make each cake and you have 200 hours this summer to devote to creating your product. Write an inequality that represents your time constraint.
*Use x as the variable
You can copy and paste the inequality sign below in your answer.
≥ < > ≤
*
1 point
j)
Solve your inequality from part i
**Make sure to have x and an inequality sign in your answer
You can copy and paste the inequality sign below in your answer.
≥ < > ≤
*
1 point
Choose the graph of the solution from part j above.
*
1 point
Option 1
Option 2
Option 3
Option 4
Other:
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
Does the investment you make and the time constraint allow you to profit from this venture?
*
1 point
Yes, I can make more than $10,000
No, I make less than $10,000
f) The revised inequality is
x ≥ 300
g) If you still sell your item for the same price, the most money you can hope to earn from your business now is $300.
h) No, you will not have to pay your parents.
i) The time constraint inequality is
2.5x ≤ 200
j) Solving the inequality from part i, the solution is
x ≤ 80
k) If you only spend the 200 hours making the cakes, your maximum total profit would be $10,000.
The investment you make and the time constraint allow you to profit from this venture.
f) The revised inequality to reflect the new spending limit is:
x ≥ 300
g) If you still sell your item for the same price, the most money you can hope to earn from your business now is $300.
h) No, you will not have to pay your parents because the additional profit is below $600.
i) The inequality representing the time constraint is:
2.5x ≤ 200
j) The solution to the inequality from part i is:
x ≤ 80
k) If you only spend the 200 hours making the cakes, your maximum total profit would be:
Profit = (50 - 14) * 200 = $7200
Yes, the investment and time constraint allow you to profit from this venture as you make more than $10,000.
f) To revise the inequality from part a to reflect the new spending limit, you need to add the additional $300 to the original spending limit of $600. This would give you a new spending limit of $900. Therefore, the revised inequality becomes:
x ≥ 900
To solve this inequality, you are looking for values of x that are greater than or equal to 900. Round to the nearest dollar means that you should only consider whole numbers. So the solution to this inequality would be x ≥ 900.
g) If you still sell your item for the same price, the most money you can hope to earn from your business now would be the amount of profit you make from selling each item multiplied by the total number of items you can make with the given resources. Since you now have 200 hours to devote to creating your product and each cake takes 2.5 hours to make, you can make a maximum of 200/2.5 = 80 cakes.
Given that the selling price of each cake is $50, the most money you can hope to earn from your business now would be 80 cakes * $50 = $4000.
h) Based on the conditions given, you will only have to pay your parents if you make more than $600 additional profit. In this case, you will have to calculate 10% of the earnings above $600. Since the most money you can hope to earn is $4000, which is less than $600, you do not have to pay your parents.
i) To represent the time constraint, you can use the inequality x * 2.5 ≤ 200. This inequality states that the product of x (the number of cakes) and the time it takes to make each cake (2.5 hours) should be less than or equal to the total available time of 200 hours.
j) To solve the inequality from part i, you need to find values of x that satisfy the constraint x * 2.5 ≤ 200. Dividing both sides of the inequality by 2.5, you get:
x ≤ 80
Therefore, the solution to this inequality is x ≤ 80.
k) If it costs $14 to make each cake and you sell them for $50 each, your maximum total profit would be the difference between the selling price and the cost to make each cake, multiplied by the number of cakes you can make. Since you can make a maximum of 80 cakes, the maximum total profit would be:
(50 - 14) * 80 = $2880.
Yes, the investment and time constraint allow you to profit from this venture, as the maximum total profit of $2880 is less than $10,000.