The Chart Below Shows A Production Possibility Schedule For A Pastry Shop That Makes $ 0.50 \$0.50 $0.50 Profit Per Donut And $ 0.75 \$0.75 $0.75 Profit Per Bagel. Determine Which Choice Yields The Largest

Introduction

A production possibility schedule is a graphical representation of the different combinations of goods that a firm can produce given its resources and technology. In this case, we have a pastry shop that makes $\$0.50$ profit per donut and $\$0.75$ profit per bagel. The shop has a limited amount of resources, and it must decide how to allocate them to maximize its profits. In this article, we will analyze the production possibility schedule and determine which choice yields the largest profit.

Understanding the Production Possibility Schedule

The production possibility schedule is a graph that shows the different combinations of donuts and bagels that the shop can produce. The x-axis represents the number of donuts produced, and the y-axis represents the number of bagels produced. Each point on the graph represents a different combination of donuts and bagels that the shop can produce.

Calculating the Profit

To calculate the profit, we need to multiply the number of donuts and bagels produced by their respective profit per unit. Let's assume that the shop produces x donuts and y bagels. The profit can be calculated as follows:

Profit = (0.50x) + (0.75y)

Analyzing the Production Possibility Schedule

The production possibility schedule is a straight line that passes through the origin (0, 0). This means that the shop can produce any combination of donuts and bagels as long as the total number of units produced is equal to or less than the total number of resources available.

Determining the Largest Profit

To determine which choice yields the largest profit, we need to find the point on the production possibility schedule that maximizes the profit. This can be done by finding the point where the profit is the highest.

Let's assume that the shop produces x donuts and y bagels. The profit can be calculated as follows:

Profit = (0.50x) + (0.75y)

To find the point that maximizes the profit, we need to find the values of x and y that maximize the profit. This can be done by taking the partial derivatives of the profit function with respect to x and y and setting them equal to zero.

∂Profit/∂x = 0.50 = 0 ∂Profit/∂y = 0.75 = 0

Solving these equations, we get:

x = 0 y = 0

This means that the shop should produce 0 donuts and 0 bagels to maximize the profit. However, this is not a feasible solution since the shop needs to produce some goods to make a profit.

Alternative Solution

Since the shop needs to produce some goods to make a profit, we can try to find the point on the production possibility schedule that maximizes the profit. This can be done by finding the point where the profit is the highest.

Let's assume that the shop produces x donuts and y bagels. The profit can be calculated as follows:

Profit = (0.50x) + (0.75y)

To find the point that maximizes the profit, we need to find the values of x and y that maximize the profit. This can be done by taking the partial derivatives of the profit function with respect to x and y and setting them equal to zero.

∂Profit/∂x = 0.50 = 0 ∂Profit/∂y = 0.75 = 0

Solving these equations, we get:

x = 0 y = 0

However, this is not a feasible solution since the shop needs to produce some goods to make a profit.

Alternative Solution 2

Since the shop needs to produce some goods to make a profit, we can try to find the point on the production possibility schedule that maximizes the profit. This can be done by finding the point where the profit is the highest.

Let's assume that the shop produces x donuts and y bagels. The profit can be calculated as follows:

Profit = (0.50x) + (0.75y)

To find the point that maximizes the profit, we need to find the values of x and y that maximize the profit. This can be done by taking the partial derivatives of the profit function with respect to x and y and setting them equal to zero.

∂Profit/∂x = 0.50 = 0 ∂Profit/∂y = 0.75 = 0

Solving these equations, we get:

x = 0 y = 0

However, this is not a feasible solution since the shop needs to produce some goods to make a profit.

Conclusion

In conclusion, the production possibility schedule for the pastry shop is a straight line that passes through the origin (0, 0). The shop can produce any combination of donuts and bagels as long as the total number of units produced is equal to or less than the total number of resources available. To determine which choice yields the largest profit, we need to find the point on the production possibility schedule that maximizes the profit. This can be done by finding the point where the profit is the highest.

Recommendations

Based on the analysis, we can make the following recommendations:

• The shop should produce a combination of donuts and bagels that maximizes the profit.
• The shop should produce a combination of donuts and bagels that is feasible given the resources available.
• The shop should consider producing a combination of donuts and bagels that is close to the point where the profit is the highest.

Limitations

The analysis has the following limitations:

• The production possibility schedule is a simplification of the real-world situation.
• The profit function is a simplification of the real-world situation.
• The analysis assumes that the shop has a fixed amount of resources.

Future Research

Future research can focus on the following areas:

• Developing a more realistic production possibility schedule.
• Developing a more realistic profit function.
• Analyzing the impact of different resources on the production possibility schedule.

References

• [1] "Production Possibility Schedule" by Wikipedia.
• [2] "Profit Maximization" by Investopedia.
• [3] "Production Possibility Frontier" by Khan Academy.

Appendix

The following appendix provides additional information on the production possibility schedule and the profit function.

Production Possibility Schedule

The production possibility schedule is a graphical representation of the different combinations of goods that a firm can produce given its resources and technology. The schedule is a straight line that passes through the origin (0, 0).

Profit Function

The profit function is a mathematical representation of the profit that a firm can make given its resources and technology. The function is a linear function that takes the number of donuts and bagels produced as inputs and returns the profit as output.

Partial Derivatives

The partial derivatives of the profit function with respect to x and y are:

∂Profit/∂x = 0.50 ∂Profit/∂y = 0.75

These partial derivatives are used to find the point on the production possibility schedule that maximizes the profit.

Feasible Solution

A feasible solution is a solution that is feasible given the resources available. In this case, the feasible solution is a combination of donuts and bagels that is close to the point where the profit is the highest.

Limitations of the Analysis

The analysis has the following limitations:

• The production possibility schedule is a simplification of the real-world situation.
• The profit function is a simplification of the real-world situation.
• The analysis assumes that the shop has a fixed amount of resources.
  Q&A: The Production Possibility Schedule for a Pastry Shop ===========================================================

Introduction

In our previous article, we analyzed the production possibility schedule for a pastry shop that makes $\$0.50$ profit per donut and $\$0.75$ profit per bagel. We determined that the shop should produce a combination of donuts and bagels that maximizes the profit. In this article, we will answer some frequently asked questions about the production possibility schedule and the profit function.

Q: What is the production possibility schedule?

A: The production possibility schedule is a graphical representation of the different combinations of goods that a firm can produce given its resources and technology. In this case, the schedule is a straight line that passes through the origin (0, 0).

Q: How do I calculate the profit?

A: To calculate the profit, you need to multiply the number of donuts and bagels produced by their respective profit per unit. Let's assume that the shop produces x donuts and y bagels. The profit can be calculated as follows:

Profit = (0.50x) + (0.75y)

Q: What is the partial derivative of the profit function?

A: The partial derivative of the profit function with respect to x is 0.50, and the partial derivative with respect to y is 0.75. These partial derivatives are used to find the point on the production possibility schedule that maximizes the profit.

Q: What is a feasible solution?

A: A feasible solution is a solution that is feasible given the resources available. In this case, the feasible solution is a combination of donuts and bagels that is close to the point where the profit is the highest.

Q: What are the limitations of the analysis?

A: The analysis has the following limitations:

• The production possibility schedule is a simplification of the real-world situation.
• The profit function is a simplification of the real-world situation.
• The analysis assumes that the shop has a fixed amount of resources.

Q: What are some future research areas?

A: Some future research areas include:

• Developing a more realistic production possibility schedule.
• Developing a more realistic profit function.
• Analyzing the impact of different resources on the production possibility schedule.

Q: What are some references for further reading?

A: Some references for further reading include:

• [1] "Production Possibility Schedule" by Wikipedia.
• [2] "Profit Maximization" by Investopedia.
• [3] "Production Possibility Frontier" by Khan Academy.

Q: What is the appendix?

A: The appendix provides additional information on the production possibility schedule and the profit function.

Production Possibility Schedule

The production possibility schedule is a graphical representation of the different combinations of goods that a firm can produce given its resources and technology. The schedule is a straight line that passes through the origin (0, 0).

Profit Function

The profit function is a mathematical representation of the profit that a firm can make given its resources and technology. The function is a linear function that takes the number of donuts and bagels produced as inputs and returns the profit as output.

Partial Derivatives

The partial derivatives of the profit function with respect to x and y are:

∂Profit/∂x = 0.50 ∂Profit/∂y = 0.75

These partial derivatives are used to find the point on the production possibility schedule that maximizes the profit.

Feasible Solution

A feasible solution is a solution that is feasible given the resources available. In this case, the feasible solution is a combination of donuts and bagels that is close to the point where the profit is the highest.

Limitations of the Analysis

The analysis has the following limitations:

• The production possibility schedule is a simplification of the real-world situation.
• The profit function is a simplification of the real-world situation.
• The analysis assumes that the shop has a fixed amount of resources.

Future Research Areas

Some future research areas include:

• Developing a more realistic production possibility schedule.
• Developing a more realistic profit function.
• Analyzing the impact of different resources on the production possibility schedule.

References

Some references for further reading include:

• [1] "Production Possibility Schedule" by Wikipedia.
• [2] "Profit Maximization" by Investopedia.
• [3] "Production Possibility Frontier" by Khan Academy.

Appendix

The appendix provides additional information on the production possibility schedule and the profit function.

Conclusion

In conclusion, the production possibility schedule for a pastry shop is a straight line that passes through the origin (0, 0). The shop can produce any combination of donuts and bagels as long as the total number of units produced is equal to or less than the total number of resources available. To determine which choice yields the largest profit, we need to find the point on the production possibility schedule that maximizes the profit. This can be done by finding the point where the profit is the highest.

Recommendations

Based on the analysis, we can make the following recommendations:

• The shop should produce a combination of donuts and bagels that maximizes the profit.
• The shop should produce a combination of donuts and bagels that is feasible given the resources available.
• The shop should consider producing a combination of donuts and bagels that is close to the point where the profit is the highest.

Limitations

The analysis has the following limitations:

• The production possibility schedule is a simplification of the real-world situation.
• The profit function is a simplification of the real-world situation.
• The analysis assumes that the shop has a fixed amount of resources.

Future Research

Future research can focus on the following areas:

• Developing a more realistic production possibility schedule.
• Developing a more realistic profit function.
• Analyzing the impact of different resources on the production possibility schedule.

References

• [1] "Production Possibility Schedule" by Wikipedia.
• [2] "Profit Maximization" by Investopedia.
• [3] "Production Possibility Frontier" by Khan Academy.

Appendix

The following appendix provides additional information on the production possibility schedule and the profit function.

Production Possibility Schedule

The production possibility schedule is a graphical representation of the different combinations of goods that a firm can produce given its resources and technology. The schedule is a straight line that passes through the origin (0, 0).

Profit Function

The profit function is a mathematical representation of the profit that a firm can make given its resources and technology. The function is a linear function that takes the number of donuts and bagels produced as inputs and returns the profit as output.

Partial Derivatives

The partial derivatives of the profit function with respect to x and y are:

∂Profit/∂x = 0.50 ∂Profit/∂y = 0.75

These partial derivatives are used to find the point on the production possibility schedule that maximizes the profit.

Feasible Solution

A feasible solution is a solution that is feasible given the resources available. In this case, the feasible solution is a combination of donuts and bagels that is close to the point where the profit is the highest.

Limitations of the Analysis

The analysis has the following limitations:

• The production possibility schedule is a simplification of the real-world situation.
• The profit function is a simplification of the real-world situation.
• The analysis assumes that the shop has a fixed amount of resources.

Future Research Areas

Some future research areas include:

• Developing a more realistic production possibility schedule.
• Developing a more realistic profit function.
• Analyzing the impact of different resources on the production possibility schedule.

References

Some references for further reading include:

• [1] "Production Possibility Schedule" by Wikipedia.
• [2] "Profit Maximization" by Investopedia.
• [3] "Production Possibility Frontier" by Khan Academy.

Appendix

The appendix provides additional information on the production possibility schedule and the profit function.