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.
* Do not include the dollar symbol in the inequality
You can copy and paste the inequality sign below in your answer.
≥ < > ≤
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1 point
x ≤ 500 + 300
Choose the graph of the solution to part f above
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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?
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1 point
h)
Will you have to pay your parents?
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Yes
No
If so, determine how much you will owe your parents.
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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.
≥ < > ≤
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1 point
j)
Solve your inequality from part i
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Choose the graph of the solution from part j above.
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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?
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Does the investment you make and the time constraint allow you to profit from this venture?
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Yes, I can make more than $10,000
No, I make less than $10,000
f) The revised inequality would be: x ≤ 500 + 300
g) The most money you can hope to earn from your business now would be $500 + $300 = $800.
h) No, you will not have to pay your parents.
i) The time constraint inequality would be: 2.5x ≤ 200
j) The graph of the solution for part i would be a line starting from the origin and sloping downwards.
k) The maximum total profit would be: Total profit = (50 - 14) * 200 = $7,200
l) Yes, the investment allows you to profit from this venture as the total profit is greater than $10,000.
f) The revised inequality is: x ≤ 500 + 300
g) The most money you can hope to earn from your business now is $800 (if you earn exactly $600 in additional profit)
h) Yes, you will have to pay your parents.
i) The inequality that represents your time constraint is: 2.5x ≤ 200
j) The solution to the inequality is: x ≤ 80
k) If you only spend the 200 hours making the cakes, your maximum total profit would be $1,200 ($50 profit per cake x 24 cakes).
The investment and time constraint do allow you to profit from this venture as you can make more than $10,000.
f) To revise the inequality to reflect the new spending limit, we need to add the additional $300 to the existing spending limit of $500. So the revised inequality would be:
x ≤ 500 + 300
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 total revenue from selling the item(s) plus the additional $300 from your parents. Since we're assuming the selling price remains the same, the most money you can hope to earn would be $500 (original profit) + $300 (additional funding) = $800.
h) To determine if you have to pay your parents, we need to check if your profit exceeds $600 after adding the additional $300. In this case, since your profit is $800, which is above $600, you will have to pay your parents.
i) To represent the time constraint, we can use the inequality:
2.5x ≤ 200
Where x represents the number of cakes you can make.
j) To solve the inequality from part i, we divide both sides of the inequality by 2.5:
x ≤ 200 / 2.5
Simplifying further:
x ≤ 80
So you can make a maximum of 80 cakes within the time constraint.
k) If you only spend the 200 hours making the cakes, your maximum total profit can be calculated by subtracting the cost of making the cakes ($14 per cake) from the selling price ($50 per cake) and then multiplying by the maximum number of cakes you can make (80):
Profit = (Selling price - Cost) * Number of cakes
= ($50 - $14) * 80
= $36 * 80
= $2,880
So your maximum total profit would be $2,880.
Regarding the last question, based on the given information, your investment and time constraint allow you to profit from this venture. However, the specific amount of profit is not provided, so we cannot conclude whether it is more or less than $10,000.
j)
Solve your inequality from part i
To solve the inequality from part i, we have:
2.5x ≤ 200
Divide both sides of the inequality by 2.5:
x ≤ 200 / 2.5
Simplify:
x ≤ 80
So the solution to the inequality is x ≤ 80.
Does the investment you make and the time constraint allow you to profit from this venture?
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1 point
Yes, I can make more than $10,000
No, I make less than $10,000