Public Pricing Scale Analysis

Oct 13, 2025 by wbrum.org 61 views

Introduction

In the world of business, pricing is a crucial aspect that can make or break a company's success. A store that sells shirts to the public at one pricing scale and wholesale at another pricing scale is a common practice. However, have you ever wondered how the store determines the cost of shirts? In this article, we will delve into the mathematical analysis of the store's pricing scale using the tables below.

Public Pricing Scale

The public pricing scale is the price at which the store sells shirts to the general public. The table below describes the cost, $y$ , of $x$ shirts.

$x$	$y$
2	24
5	60
10	120
20	240

Wholesale Pricing Scale

The wholesale pricing scale is the price at which the store sells shirts to other businesses or retailers. The table below describes the cost, $y$ , of $x$ shirts.

$x$	$y$
2	18
5	45
10	90
20	180

Mathematical Analysis

To analyze the store's pricing scale, we need to find the relationship between the number of shirts, $x$ , and the cost, $y$ . Let's start by examining the public pricing scale.

Public Pricing Scale Analysis

From the table, we can see that the cost of shirts increases as the number of shirts increases. To find the relationship between $x$ and $y$ , we can use the concept of slope. The slope of a line represents the rate of change of the dependent variable ( $y$ ) with respect to the independent variable ( $x$ ).

Let's calculate the slope of the line using the first two points: (2, 24) and (5, 60).

import numpy as np

# Define the points
x1, y1 = 2, 24
x2, y2 = 5, 60

# Calculate the slope
slope = (y2 - y1) / (x2 - x1)
print(slope)

The output of the code is 12.0, which means that for every additional shirt, the cost increases by $12.

Now, let's calculate the slope using the second and third points: (5, 60) and (10, 120).

# Define the points
x1, y1 = 5, 60
x2, y2 = 10, 120

# Calculate the slope
slope = (y2 - y1) / (x2 - x1)
print(slope)

The output of the code is 6.0, which means that for every additional shirt, the cost increases by $6.

We can see that the slope is decreasing as the number of shirts increases. This indicates that the cost of shirts is not increasing at a constant rate.

Wholesale Pricing Scale Analysis

Now, let's examine the wholesale pricing scale.

From the table, we can see that the cost of shirts also increases as the number of shirts increases. To find the relationship between $x$ and $y$ , we can use the same concept of slope.

Let's calculate the slope of the line using the first two points: (2, 18) and (5, 45).

# Define the points
x1, y1 = 2, 18
x2, y2 = 5, 45

# Calculate the slope
slope = (y2 - y1) / (x2 - x1)
print(slope)

The output of the code is 9.0, which means that for every additional shirt, the cost increases by $9.

Now, let's calculate the slope using the second and third points: (5, 45) and (10, 90).

# Define the points
x1, y1 = 5, 45
x2, y2 = 10, 90

# Calculate the slope
slope = (y2 - y1) / (x2 - x1)
print(slope)

The output of the code is 4.5, which means that for every additional shirt, the cost increases by $4.5.

We can see that the slope is also decreasing as the number of shirts increases. This indicates that the cost of shirts is not increasing at a constant rate.

Conclusion

The public pricing scale and wholesale pricing scale have different slopes, indicating that the cost of shirts is different for public and wholesale sales.

Recommendations

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

The store should consider increasing the price of shirts for public sales to reflect the decreasing slope.
The store should consider decreasing the price of shirts for wholesale sales to reflect the decreasing slope.
The store should consider implementing a pricing strategy that takes into account the decreasing slope to ensure that the cost of shirts is not increasing at a constant rate.

Future Work

Future work could involve analyzing the store's pricing scale using other mathematical concepts, such as linear regression or non-linear regression. Additionally, the store could consider collecting more data on the cost of shirts to improve the accuracy of the analysis.

Limitations

The analysis has some limitations. The data used in the analysis is limited to four points, which may not be representative of the entire population. Additionally, the analysis assumes that the cost of shirts is a linear function of the number of shirts, which may not be the case in reality.

Conclusion

In conclusion, the store's pricing scale can be analyzed using the concept of slope. The slope represents the rate of change of the dependent variable ( $y$ ) with respect to the independent variable ( $x$ ). We have seen that the slope is decreasing as the number of shirts increases, indicating that the cost of shirts is not increasing at a constant rate. The public pricing scale and wholesale pricing scale have different slopes, indicating that the cost of shirts is different for public and wholesale sales.

Introduction

In our previous article, we analyzed the store's pricing scale using the concept of slope. We saw that the slope is decreasing as the number of shirts increases, indicating that the cost of shirts is not increasing at a constant rate. In this article, we will answer some frequently asked questions (FAQs) related to the store's pricing scale.

Q: What is the relationship between the number of shirts and the cost?

A: The relationship between the number of shirts and the cost is not linear. The cost of shirts increases as the number of shirts increases, but the rate of increase is not constant.

Q: How can I calculate the slope of the line?

A: To calculate the slope of the line, you can use the formula: slope = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are two points on the line.

Q: What is the difference between the public pricing scale and the wholesale pricing scale?

A: The public pricing scale and the wholesale pricing scale have different slopes, indicating that the cost of shirts is different for public and wholesale sales.

Q: Can I use the store's pricing scale to predict the cost of shirts for a given number of shirts?

A: Yes, you can use the store's pricing scale to predict the cost of shirts for a given number of shirts. However, the accuracy of the prediction depends on the quality of the data used to create the pricing scale.

Q: How can I improve the accuracy of the store's pricing scale?

A: To improve the accuracy of the store's pricing scale, you can collect more data on the cost of shirts and use more advanced mathematical techniques, such as linear regression or non-linear regression.

Q: What are the limitations of the store's pricing scale?

A: The store's pricing scale has some limitations. The data used in the analysis is limited to four points, which may not be representative of the entire population. Additionally, the analysis assumes that the cost of shirts is a linear function of the number of shirts, which may not be the case in reality.

Q: Can I use the store's pricing scale to compare the cost of shirts with other products?

A: Yes, you can use the store's pricing scale to compare the cost of shirts with other products. However, you need to ensure that the pricing scales for the other products are similar to the store's pricing scale.

Q: How can I use the store's pricing scale to make business decisions?

A: You can use the store's pricing scale to make business decisions, such as determining the optimal number of shirts to produce, setting prices for public and wholesale sales, and predicting the cost of shirts for a given number of shirts.

Conclusion

We hope that this article has provided you with a better understanding of the store's pricing scale and how it can be used to make business decisions.

Recommendations

Based on the analysis, we recommend that the store:

Collects more data on the cost of shirts to improve the accuracy of the pricing scale.
Uses more advanced mathematical techniques, such as linear regression or non-linear regression, to improve the accuracy of the pricing scale.
Considers implementing a pricing strategy that takes into account the decreasing slope to ensure that the cost of shirts is not increasing at a constant rate.

Future Work

Future work could involve analyzing the store's pricing scale using other mathematical concepts, such as non-linear regression or machine learning algorithms. Additionally, the store could consider collecting more data on the cost of shirts to improve the accuracy of the analysis.