Yaster Outfitters manufactures and sells extreme-cold sleeping bags. The table below shows the price-demand and total cost data, where: D . p is the wholesale price (in dollars) of a sleeping bag for a weekly demand of a sleeping bags; . C is the total cost (in dollars) of producing a sleeping bags. C ($) 13,000 14,300 18,500 21,000 Use this data to create regression models to answer all of the questions below. x (sleeping bags) 95 120 180 220 P ($) 240 235 155 50 Price Model Find a quadratic regression equation for the price-demand data, using a as the independent variable. p= a +bx+cx² Round a to the nearest integer, round b to 2 decimal places, and round c to 4 decimal places. Use this price model to answer question 1-2 below.

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### Analysis of Price-Demand and Production Cost Data for Yaster Outfitters

**Overview:**
Yaster Outfitters manufactures and sells extreme-cold sleeping bags. The table below showcases the data of their price-demand and total cost analysis, where:
- \( p \) represents the wholesale price (in dollars) of a sleeping bag for a weekly demand of \( x \) sleeping bags.
- \( C \) denotes the total cost (in dollars) of producing \( x \) sleeping bags.

**Data Table:**
| x (sleeping bags) | p ($) | C ($)   |
|-------------------|-------|---------|
| 95                | 240   | 13,000  |
| 120               | 235   | 14,300  |
| 180               | 155   | 18,500  |
| 220               |  50   | 21,000  |

This dataset serves as a basis to create regression models to answer various analytical questions regarding price, demand, and production costs.

### Price Model

To determine the relationship between the price and the demand for sleeping bags, we will develop a quadratic regression equation based on the given data. The independent variable will be \( x \) (number of sleeping bags).

**Quadratic Regression Model Equation:**
\[ p = a + bx + cx^2 \]

**Instructions:**
- **Round \( a \) to the nearest integer.**
- **Round \( b \) to two decimal places.**
- **Round \( c \) to four decimal places.**

**Objective:**
Use this price model equation to answer the following questions:

**Questions:**
1. Calculate the predicted price for a given demand.
2. Analyze how changes in demand affect the wholesale price.

Utilize the provided data and the quadratic regression model to perform detailed analytical calculations and derive meaningful insights for decision-making at Yaster Outfitters.
Transcribed Image Text:### Analysis of Price-Demand and Production Cost Data for Yaster Outfitters **Overview:** Yaster Outfitters manufactures and sells extreme-cold sleeping bags. The table below showcases the data of their price-demand and total cost analysis, where: - \( p \) represents the wholesale price (in dollars) of a sleeping bag for a weekly demand of \( x \) sleeping bags. - \( C \) denotes the total cost (in dollars) of producing \( x \) sleeping bags. **Data Table:** | x (sleeping bags) | p ($) | C ($) | |-------------------|-------|---------| | 95 | 240 | 13,000 | | 120 | 235 | 14,300 | | 180 | 155 | 18,500 | | 220 | 50 | 21,000 | This dataset serves as a basis to create regression models to answer various analytical questions regarding price, demand, and production costs. ### Price Model To determine the relationship between the price and the demand for sleeping bags, we will develop a quadratic regression equation based on the given data. The independent variable will be \( x \) (number of sleeping bags). **Quadratic Regression Model Equation:** \[ p = a + bx + cx^2 \] **Instructions:** - **Round \( a \) to the nearest integer.** - **Round \( b \) to two decimal places.** - **Round \( c \) to four decimal places.** **Objective:** Use this price model equation to answer the following questions: **Questions:** 1. Calculate the predicted price for a given demand. 2. Analyze how changes in demand affect the wholesale price. Utilize the provided data and the quadratic regression model to perform detailed analytical calculations and derive meaningful insights for decision-making at Yaster Outfitters.
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