Unit 4 Portfolio Part 1
You want to start a bakery business to earn money. The total amount of money you will invest is $10,000. You will be selling cakes. It will cost you $14 to make each cake.
a)
Write an inequality that represents the cost of making x amount of cakes should not exceed this investment.
* Do not include the dollar symbol in the inequality
You can copy and paste the inequality sign below in your answer.
≥ < > ≤
*
1 point
14x≤10000
b)
Solve this inequality and choose the graph of the solution.
* Make sure to round to the nearest whole number.
Do not include dollar signs in the solution
*
1 point
x≤714
Choose the graph of the solution to part b above.
1 point
Captionless Image
Option A
Option B
Option C
Option D
c)
You plan to sell each cake for $50. Write an equation that represents your total earnings, T, based on the price of your cake and how many you sell. Let x represent the number of cakes you sell.
* Use T and x as your variables
*
1 point
d)
Using your answer from part b and your equation from part c, what is the most money you can hope to earn from your business?
*
1 point
e)
Don’t forget that at the beginning of the process you had to spend some of your own money to get started. With the costs taken into account, what was your total profit?
*
1 point
Did you make money or lose money?
*
1 point
Make Money
Lose Money
a) The inequality that represents the cost of making x amount of cakes should not exceed the investment of $10,000 is:
14x ≤ 10000
b) To solve the inequality, divide both sides of the inequality by 14:
14x/14 ≤ 10000/14
x ≤ 714 (rounded to the nearest whole number)
The graph of the solution is:
Option B
c) The equation that represents the total earnings T based on the price of each cake ($50) and the number of cakes sold (x) is:
T = 50x
d) Since x can be at most 714 (from part b), substitute x = 714 into the equation from part c to find the most money you can hope to earn:
T = 50 * 714
T = $35,700 (rounded to the nearest whole number)
e) To calculate the total profit, subtract the total cost of making the cakes from the total earnings:
Total Cost = 14 * 714 = $9,996 (rounded to the nearest whole number)
Total Profit = Total Earnings - Total Cost
Total Profit = $35,700 - $9,996
Total Profit = $25,704
You made money with a total profit of $25,704.
c) T = 50x
d) The most money that can be earned from the business is $35,700.
e) The total profit is $25,700. The business made money.
Don’t forget that at the beginning of the process you had to spend some of your own money to get started. With the costs taken into account, what was your total profit?
To calculate the total profit, we need to subtract the initial investment from the total earnings. The initial investment was $10,000.
Total Profit = Total Earnings - Initial Investment
Total Profit = $35,700 - $10,000
Total Profit = $25,700
After taking into account the initial investment, the total profit is $25,700.
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.
≥ < > ≤
*
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
*
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 to reflect the new spending limit with an additional $300 is:
14x ≤ 10300
To solve this inequality, divide both sides by 14:
14x/14 ≤ 10300/14
x ≤ 735
The graph of the solution is:
Option B
g) If you still sell your items for the same price, the most money you can hope to earn from your business now is:
$36,750 (735 cakes * $50 per cake)
h) Yes, you will have to pay your parents since you will make more than $600 additional profit.
i) The inequality that represents the time constraint of 2.5 hours per cake and 200 hours available is:
2.5x ≤ 200
j) To solve this inequality, divide both sides by 2.5:
2.5x/2.5 ≤ 200/2.5
x ≤ 80
The graph of the solution is:
Option 1
k) If you spend the 200 hours making the cakes, your maximum total profit would be:
Total Profit = (735 cakes - 200 hours) * $36 per cake
Total Profit = 535 cakes * $36
Total Profit = $19,260
The investment and time constraint allow you to profit from this venture, but the profit is less than $10,000.