A company produces two types of hand soaps: a solid and a liquid soap. The cost of production for a solid soap is 10 cents per soap and 20 cents for the liquid soap. The company developed a model that predicts how many units x1 (of the solid soap), and x2 (of the liquid soap) they will sell per month. According to the model, the amount of units sold depends on the prices p1,p2 (in dollars) of solid and liquid soap through the equation (EQUATION IS ATTACHED)Find the total profit if the price of the solid soap is $1 and the price of the liquid soap is $2. The image contains two linear equations representing demand functions:1. $ x_1 = 200 + 100(p_2 - p_1) $2. $ x_2 = 500 - 150p_2 $**Explanation of Equations:**- **Equation 1: $ x_1 = 200 + 100(p_2 - p_1) $** - This equation calculates $ x_1 $, the quantity demanded of a good or service. - It is determined by a base demand of 200 units plus an adjustment factor involving the price difference $ (p_2 - p_1) $. Here, $ p_2 $ and $ p_1 $ might represent the prices of two related goods or the current and a reference price, respectively. - The coefficient 100 indicates the sensitivity of the quantity demanded to changes in the price difference.- **Equation 2: $ x_2 = 500 - 150p_2 $** - This equation calculates $ x_2 $, another quantity demanded. - It starts with a base demand of 500 units, which decreases by 150 units for every one unit increase in the price $ p_2 $. - The coefficient 150 shows the responsiveness of the quantity demanded to the price $ p_2 $.These equations are useful in economic analysis to understand how price changes affect the quantity demanded of goods. They can be applied in various contexts like market studies, pricing strategies, or consumer behavior analysis.

Given that the cost of production of 1 unit of solid soap is 10 cents = 0.1 dollars and the cost of…

Answered: A company produces two types of hand…

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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A company produces two types of hand soaps: a solid and a liquid soap. The cost of production for a solid soap is 10 cents per soap and 20 cents for the liquid soap. The company developed a model that predicts how many units x1 (of the solid soap), and x2 (of the liquid soap) they will sell per month. According to the model, the amount of units sold depends on the prices p1,p2 (in dollars) of solid and liquid soap through the equation (EQUATION IS ATTACHED)

Find the total profit if the price of the solid soap is $1 and the price of the liquid soap is $2.

The image contains two linear equations representing demand functions:

1. $ x_1 = 200 + 100(p_2 - p_1) $
2. $ x_2 = 500 - 150p_2 $

**Explanation of Equations:**

- **Equation 1: $ x_1 = 200 + 100(p_2 - p_1) $**
- This equation calculates $ x_1 $, the quantity demanded of a good or service.
- It is determined by a base demand of 200 units plus an adjustment factor involving the price difference $ (p_2 - p_1) $. Here, $ p_2 $ and $ p_1 $ might represent the prices of two related goods or the current and a reference price, respectively.
- The coefficient 100 indicates the sensitivity of the quantity demanded to changes in the price difference.

- **Equation 2: $ x_2 = 500 - 150p_2 $**
- This equation calculates $ x_2 $, another quantity demanded.
- It starts with a base demand of 500 units, which decreases by 150 units for every one unit increase in the price $ p_2 $.
- The coefficient 150 shows the responsiveness of the quantity demanded to the price $ p_2 $.

These equations are useful in economic analysis to understand how price changes affect the quantity demanded of goods. They can be applied in various contexts like market studies, pricing strategies, or consumer behavior analysis.

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