**Cost, Revenue & Profit***For these problems, $ x $ will represent the number of items and $ y $ will represent the money.*The fixed costs for a certain item are $215 per week. The cost to produce each item is $5 per item.Using this information, what is the cost equation? Give your answer in slope-intercept form: \[ y = 3x + 100 \]The retailer intends to sell each item for $8/item.Using this information, what is the revenue equation? Give your answer in slope-intercept form: \[ y = 8(50) x \]If in this week 50 items are made and sold in the week, what are the total costs to the retailer?---### Explanation of Graphs and Diagrams**Image Content:**- The image contains problems about cost, revenue, and profit calculations.- It specifies fixed costs, variable costs, and selling prices per item.- Equations are to be formulated in the slope-intercept form.**Key Concepts:****1. Cost Equation:** - Fixed Costs: $215 per week - Variable Costs: $5 per item produced - Cost Equation: \[ y = 5x + 215 \] Here, $ y $ is the total cost, and $ x $ is the number of items produced. **2. Revenue Equation:** - Selling Price: $8 per item - Revenue Equation: \[ y = 8x \] Here, $ y $ is the total revenue, and $ x $ is the number of items sold. **Example Calculation:**- If 50 items are made and sold: - Total Cost: \[ y = 5 \cdot 50 + 215 = 250 + 215 = 465 \] - Total Revenue: \[ y = 8 \cdot 50 = 400 \] This document provides a clear explanation and step-by-step guide to formulating cost and revenue equations in an algebraic context, suitable for educational purposes.

We will find the cost equation and revenue equation as following.

Cost, Revenue & Profit For these problems, x will represent the number of items and y will represent the money. The fixed costs for a certain item are $215 per week. The cost to produce each item is $5 per item. Using this information, what is the cost equation? Give your answer in slope-intercept form: Y = 3x + 100 The retailer intends to sell each item for $8/item. Using this information, what is the revenue equation? Give your answer in slope-intercept form: y = 8(50)

Cost, Revenue & Profit For these problems, x will represent the number of items and y will represent the money. The fixed costs for a certain item are $215 per week. The cost to produce each item is $5 per item. Using this information, what is the cost equation? Give your answer in slope-intercept form: Y = 3x + 100 The retailer intends to sell each item for $8/item. Using this information, what is the revenue equation? Give your answer in slope-intercept form: y = 8(50)

Algebra and Trigonometry (6th Edition)

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

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Equations and Inequations

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A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.

Question

**Cost, Revenue & Profit**

*For these problems, $ x $ will represent the number of items and $ y $ will represent the money.*

The fixed costs for a certain item are $215 per week. The cost to produce each item is $5 per item.

Using this information, what is the cost equation? Give your answer in slope-intercept form:
\[ y = 3x + 100 \]

The retailer intends to sell each item for $8/item.

Using this information, what is the revenue equation? Give your answer in slope-intercept form:
\[ y = 8(50) x \]

If in this week 50 items are made and sold in the week, what are the total costs to the retailer?

---

### Explanation of Graphs and Diagrams

**Image Content:**

- The image contains problems about cost, revenue, and profit calculations.
- It specifies fixed costs, variable costs, and selling prices per item.
- Equations are to be formulated in the slope-intercept form.

**Key Concepts:**

**1. Cost Equation:**
- Fixed Costs: $215 per week
- Variable Costs: $5 per item produced
- Cost Equation:
\[ y = 5x + 215 \]
Here, $ y $ is the total cost, and $ x $ is the number of items produced.

**2. Revenue Equation:**
- Selling Price: $8 per item
- Revenue Equation:
\[ y = 8x \]
Here, $ y $ is the total revenue, and $ x $ is the number of items sold.

**Example Calculation:**
- If 50 items are made and sold:
- Total Cost:
\[ y = 5 \cdot 50 + 215 = 250 + 215 = 465 \]
- Total Revenue:
\[ y = 8 \cdot 50 = 400 \]

This document provides a clear explanation and step-by-step guide to formulating cost and revenue equations in an algebraic context, suitable for educational purposes.

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