Question
Can you change this function: Innovative Technology Impact
New Profit Function Post-Innovation
Following the introduction of innovative technology, there’s a sustained increase in profits due to improved customer engagement and sales management.
New Profit Function Q(t):
- Q(t) = { 200000, 0 ≤ t < 4
300000, t = 4
300000, 4 < t ≤ 8
275000, 8 < t ≤ 10 }
to fit my project:
I would do a video game business that sells all kinds of gaming merchandise. Here are the basics
Business name: Game Paradise
The Provided Goods and Services
Games: we would sell games downloadable and playable across all types of platforms, such as PC’s, Xbox, PlayStation, and Nintendo. (An example is Stunt Paradise, which is adaptable to almost all platforms)
Consoles: We’d have to sell consoles for the games, so of course we would sell game consoles and also things like computers for PC games and such.
We would also sell accessories, such as controllers, headphones, keyboards and mouses, charging stations, etc.
We would have a program that gives customers credit for bringing in consoles, games, merch, etc. It would either give customers points off of their next purchase, or on-the-spot payments, customer’s choice.
We would also host gaming nights, where people could pay to join in video game tournaments and such.
Estimates for the Starting Costs
The starting inventory price could be between 25,000 dollars to 50,000 dollars. I will say 40,000 dollars seems like a decent investment for starting up the business.
I would spend about 10-20,000 dollars investing in furniture such as shelves, bookcases, racks, etc. I’d say about 15,000 ought to do.
The lease/rent prices for the lot for the first year would prob. be about 12-24,000 dollars a year, considering it could be about 1-2,000 dollars a month. I’d say about 12,000 dollars.
For online and local advertising I would throw in about 7,000 dollars.
And the operating expenses and utilities would probably cost me about 5-10,000 dollars for a really great bang for a start, so I’d invest about 8,000 dollars.
Overall cost: 82,000
My budget would be to not go over 82,000 dollars, and stay under my limit if possible.
Pricing
A new game would probably go for thirty bucks, so people would appreciate my prices and come back for more.
A used game could go for fifteen bucks, since some might not be good and maybe a little scratched.
As for consoles and PC’s, 300 dollars for a new consoles, 150 for a new PC, 150 for a refurbished and/or used console, 75 for a refurbished and/or used PC.
A game accessory could go for about 20 dollars on an average, ten bucks bottom line.
For tournaments, little kids 10 and under get in free, but the admission fee for anyone older is 10 dollars.
Members and Loyalty customers would get 5% off everything they purchase or buy access to.
Revenue Example
Here is an example of the sale-per-month
100 new games purchased: 3,000 dollars
150 used games purchased: 2,250 dollars
10 new gaming consoles purchased: 3,000 dollars
20 new gaming PC’s purchased: 3,000
5 Refurbished/Used consoles purchased: 750 dollars
10 refurbished/used PC’s Purchased: 750 dollars
75 accessories purchased: 750 – 1,500 dollars
4 event nights with about 30 adult participants each: 1,200
Monthly Revenue Approx.: 14,700 - 15,450
Yearly Revenue Approx.: 176,400-185,400
The Profit Calculation
Let’s say our monthly revenue is 15,450.
And our Monty Operation Expense is about 4,500 dollars.
Monthly Profit: 15,450 (Revenue) – 4,500 (Expenses) = 10,950
Yearly Profit: 10,950 X 12 = 131,400
So my yearly profit would be 131,400
The Function For My 10-Year Profit
Years 1-3 will have a slow growth
At Approx. 150,000 dollars a year.
Year 4 would introduce new technology to my business, such as inventory management, new game devices such as VR, etc.
The Profit would be about 250,000 sales because of better efficiency and better, speedy sales, etc.
Years 5-10 would feature a more sustained growth, because of loyalty and repeated customers such as local kids coming back for more games.
The Profit could estimate to about 200,000 dollars per year.
Here is your function.
Profit Function P (t):
- P (t) = {150,000, 0 ≤ t < 4
250,000, t = 4
200,000, 4 < t ≤ 10}
Graph Description”
On a graph with years on the x-axis and profit on the y-axis, you'll see: A steady line at $150,000 for Years 1-3,
A spike to $250,000 at Year 4,
A line at $200,000 from Years 5 to 10.
New Profit Function Post-Innovation
Following the introduction of innovative technology, there’s a sustained increase in profits due to improved customer engagement and sales management.
New Profit Function Q(t):
- Q(t) = { 200000, 0 ≤ t < 4
300000, t = 4
300000, 4 < t ≤ 8
275000, 8 < t ≤ 10 }
to fit my project:
I would do a video game business that sells all kinds of gaming merchandise. Here are the basics
Business name: Game Paradise
The Provided Goods and Services
Games: we would sell games downloadable and playable across all types of platforms, such as PC’s, Xbox, PlayStation, and Nintendo. (An example is Stunt Paradise, which is adaptable to almost all platforms)
Consoles: We’d have to sell consoles for the games, so of course we would sell game consoles and also things like computers for PC games and such.
We would also sell accessories, such as controllers, headphones, keyboards and mouses, charging stations, etc.
We would have a program that gives customers credit for bringing in consoles, games, merch, etc. It would either give customers points off of their next purchase, or on-the-spot payments, customer’s choice.
We would also host gaming nights, where people could pay to join in video game tournaments and such.
Estimates for the Starting Costs
The starting inventory price could be between 25,000 dollars to 50,000 dollars. I will say 40,000 dollars seems like a decent investment for starting up the business.
I would spend about 10-20,000 dollars investing in furniture such as shelves, bookcases, racks, etc. I’d say about 15,000 ought to do.
The lease/rent prices for the lot for the first year would prob. be about 12-24,000 dollars a year, considering it could be about 1-2,000 dollars a month. I’d say about 12,000 dollars.
For online and local advertising I would throw in about 7,000 dollars.
And the operating expenses and utilities would probably cost me about 5-10,000 dollars for a really great bang for a start, so I’d invest about 8,000 dollars.
Overall cost: 82,000
My budget would be to not go over 82,000 dollars, and stay under my limit if possible.
Pricing
A new game would probably go for thirty bucks, so people would appreciate my prices and come back for more.
A used game could go for fifteen bucks, since some might not be good and maybe a little scratched.
As for consoles and PC’s, 300 dollars for a new consoles, 150 for a new PC, 150 for a refurbished and/or used console, 75 for a refurbished and/or used PC.
A game accessory could go for about 20 dollars on an average, ten bucks bottom line.
For tournaments, little kids 10 and under get in free, but the admission fee for anyone older is 10 dollars.
Members and Loyalty customers would get 5% off everything they purchase or buy access to.
Revenue Example
Here is an example of the sale-per-month
100 new games purchased: 3,000 dollars
150 used games purchased: 2,250 dollars
10 new gaming consoles purchased: 3,000 dollars
20 new gaming PC’s purchased: 3,000
5 Refurbished/Used consoles purchased: 750 dollars
10 refurbished/used PC’s Purchased: 750 dollars
75 accessories purchased: 750 – 1,500 dollars
4 event nights with about 30 adult participants each: 1,200
Monthly Revenue Approx.: 14,700 - 15,450
Yearly Revenue Approx.: 176,400-185,400
The Profit Calculation
Let’s say our monthly revenue is 15,450.
And our Monty Operation Expense is about 4,500 dollars.
Monthly Profit: 15,450 (Revenue) – 4,500 (Expenses) = 10,950
Yearly Profit: 10,950 X 12 = 131,400
So my yearly profit would be 131,400
The Function For My 10-Year Profit
Years 1-3 will have a slow growth
At Approx. 150,000 dollars a year.
Year 4 would introduce new technology to my business, such as inventory management, new game devices such as VR, etc.
The Profit would be about 250,000 sales because of better efficiency and better, speedy sales, etc.
Years 5-10 would feature a more sustained growth, because of loyalty and repeated customers such as local kids coming back for more games.
The Profit could estimate to about 200,000 dollars per year.
Here is your function.
Profit Function P (t):
- P (t) = {150,000, 0 ≤ t < 4
250,000, t = 4
200,000, 4 < t ≤ 10}
Graph Description”
On a graph with years on the x-axis and profit on the y-axis, you'll see: A steady line at $150,000 for Years 1-3,
A spike to $250,000 at Year 4,
A line at $200,000 from Years 5 to 10.
Answers
Answered by
GPT-4o mini
Here’s the modified profit function tailored for your video game business, Game Paradise. This function reflects the steady growth, introduction of innovative technology, and sustained profit that you provided in your description:
### Profit Function P(t) for Game Paradise
\[
P(t) =
\begin{cases}
150,000 & \text{for } 0 \leq t < 4 \\
250,000 & \text{for } t = 4 \\
200,000 & \text{for } 4 < t \leq 10
\end{cases}
\]
### Graph Description
On a graph with years on the x-axis and profit on the y-axis:
- **Years 1-3 (0 ≤ t < 4)**: You will see a steady line at $150,000, indicating steady growth in profits as the business establishes itself.
- **Year 4 (t = 4)**: This year will show a spike to $250,000, representing a significant increase due to the introduction of innovative technologies (such as inventory management systems and new gaming devices like VR).
- **Years 5-10 (4 < t ≤ 10)**: The graph will show a line at $200,000 during these years, reflecting sustained profit growth fueled by increased customer loyalty and repeat business from local customers.
### Summary
This profit function allows you to visualize expected profit trends for Game Paradise over a 10-year period, supporting strategic planning and decision-making based on your innovative growth and established customer base.
### Profit Function P(t) for Game Paradise
\[
P(t) =
\begin{cases}
150,000 & \text{for } 0 \leq t < 4 \\
250,000 & \text{for } t = 4 \\
200,000 & \text{for } 4 < t \leq 10
\end{cases}
\]
### Graph Description
On a graph with years on the x-axis and profit on the y-axis:
- **Years 1-3 (0 ≤ t < 4)**: You will see a steady line at $150,000, indicating steady growth in profits as the business establishes itself.
- **Year 4 (t = 4)**: This year will show a spike to $250,000, representing a significant increase due to the introduction of innovative technologies (such as inventory management systems and new gaming devices like VR).
- **Years 5-10 (4 < t ≤ 10)**: The graph will show a line at $200,000 during these years, reflecting sustained profit growth fueled by increased customer loyalty and repeat business from local customers.
### Summary
This profit function allows you to visualize expected profit trends for Game Paradise over a 10-year period, supporting strategic planning and decision-making based on your innovative growth and established customer base.