# Find Optimal t for Profit: C vs. R

• MHB
• alllove
In summary, to generate a profit, the revenue generated from sales must be greater than the cost of producing t units. This can be represented by the inequality 4t^2 + t > 3t^2 + 9t. To determine the number of units to be sold in order to generate a profit, we can set this inequality equal to 0 and solve for t. This results in t^2 - 8t = 0, indicating that the break even point is at t = 0 or t = 8. Therefore, the number of units to be sold in order to generate a profit is t > 8.
alllove
The cost of producing t units is C = 3t2 + 9t, and the revenue generated from sales is R = 4t2 + t. Determine the number of units to be sold in order to generate a profit.

Select one:
A. t > 8
B. t > 10
C. t > 9
D. t > 0

For the profit we must have $R > C$

or $4t^2+t > 3t^2 + 9t$

Now you can proceed from here and find the result

Another way of looking at it: "profit" is "revenue minus costs", R- C= 4t^2+ t- (3t^2+ 9t)= t^2- 8t. The "break even" point, separating "loss" and "profit" is where that is 0. Solve t^2- 8t= 0.

(Using "^" to indicate powers makes it easier to read: "t^2" rather than "t2".)

## 1. What is the purpose of finding the optimal t for profit in the C vs. R scenario?

The purpose of finding the optimal t for profit is to determine the best time to transition from using a traditional product (C) to a new, potentially more profitable product (R). This decision can greatly impact the success and profitability of a company.

## 2. How is the optimal t for profit calculated?

The optimal t for profit is typically calculated using mathematical models and data analysis techniques. These models take into account factors such as production costs, market demand, and potential revenue to determine the most profitable time to transition from C to R.

## 3. What are some potential challenges in finding the optimal t for profit?

Some potential challenges in finding the optimal t for profit include uncertainty in market demand, fluctuations in production costs, and the potential for unforeseen obstacles that may affect the transition process. Additionally, different models and data analysis techniques may yield varying results, making it important to carefully consider and validate the chosen approach.

## 4. How does finding the optimal t for profit benefit a company?

Finding the optimal t for profit can greatly benefit a company by maximizing profitability and minimizing potential losses. It allows for a strategic and data-driven decision-making process, ensuring that the transition from C to R is timed appropriately and effectively. This can also improve the company's competitive advantage and overall success in the market.

## 5. Are there any limitations to using the optimal t for profit approach?

While finding the optimal t for profit can be a valuable tool for decision-making, it is important to note that it is not a guarantee of success. It is based on assumptions and predictions, which may not always accurately reflect real-world scenarios. Additionally, external factors such as changes in market trends or unexpected events can impact the outcome. It is important for companies to regularly review and adjust their strategies to adapt to changing circumstances.

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