a) It costs $1500 plus $5.00 per bottle to produce the lotion. If x represents the number of bottles and y represent the amount of money, the equation that models this scenario is y = 5x + 1500 [Hint: Lesson 6.4, Lesson 5.2, Lesson 4.3, Lesson 2.2, Lesson 7.1] What does the rate of change and the initial condition represent in this scenario? ii) The company has $2 500, solve the equation to determine the number of lotion bottles that can be made.
a) It costs $1500 plus $5.00 per bottle to produce the lotion. If x represents the number of bottles and y represent the amount of money, the equation that models this scenario is y = 5x + 1500 [Hint: Lesson 6.4, Lesson 5.2, Lesson 4.3, Lesson 2.2, Lesson 7.1] What does the rate of change and the initial condition represent in this scenario? ii) The company has $2 500, solve the equation to determine the number of lotion bottles that can be made.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question
![Question 4
a) It costs $1500 plus $5.00 per bottle to produce the lotion.
If x represents the number of bottles and y represent the amount of money, the equation that models this
scenario is y = 5x + 1500
[Hint: Lesson 6.4, Lesson 5.2, Lesson 4.3, Lesson 2.2, Lesson 7.1]
1)
What does the rate of change and the initial condition represent in this scenario?
ii)
The company has $2 500, solve the equation to determine the number of lotion bottles that can
be made.
b) Each bottle of lotion sells for $20.00.
If x represents the number of bottles and y represent the amount of money, the equation that models this
scenario is y = 20x
i)
Would this represent a direct or inverse variation? (Explain your answer)
ii)
Terry likes the product and would like to buy 10 bottles, how much money would she spend?
c) The company dropped the price of the lotion to $15.00 per bottle for Boxing Day Sale. Write an
equation that models the sale of the lotion bottles?
d) The equation that represents the profit is y=20x-(5x+1500)
Simplify this equation
e) Use the equation to determine the number of lotion bottles that would have to be sold to make a profit of
$600.
4](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd672829b-f6c8-47b6-8835-d8cd4f1626a8%2Fbf7ab5b6-316e-4489-95e1-fa6941108ab5%2Fz99tu7b_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Question 4
a) It costs $1500 plus $5.00 per bottle to produce the lotion.
If x represents the number of bottles and y represent the amount of money, the equation that models this
scenario is y = 5x + 1500
[Hint: Lesson 6.4, Lesson 5.2, Lesson 4.3, Lesson 2.2, Lesson 7.1]
1)
What does the rate of change and the initial condition represent in this scenario?
ii)
The company has $2 500, solve the equation to determine the number of lotion bottles that can
be made.
b) Each bottle of lotion sells for $20.00.
If x represents the number of bottles and y represent the amount of money, the equation that models this
scenario is y = 20x
i)
Would this represent a direct or inverse variation? (Explain your answer)
ii)
Terry likes the product and would like to buy 10 bottles, how much money would she spend?
c) The company dropped the price of the lotion to $15.00 per bottle for Boxing Day Sale. Write an
equation that models the sale of the lotion bottles?
d) The equation that represents the profit is y=20x-(5x+1500)
Simplify this equation
e) Use the equation to determine the number of lotion bottles that would have to be sold to make a profit of
$600.
4
Transcribed Image Text:How much profit would be 50 bottles of lotion were sold? 1
Based on your answer to f(1), what does that indicate about the profit?
g) Mrs. Parkes decided to expand her company. The graph below represents the cost to make the lotion and
amount made selling the lotion. The lotions are still sold for $20.00 per bottle
Cost and Sales of Lotion
25000-
Cost
20000.
15000
10000
5000
i)
Amount of Money ($)
Sales
0
500
1000
1500
Number of Lotion Bottles
Write an equation to represent the new cost of making the lotion.
How many lotion bottles must be sold to break even?
2000
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