Question
Cost, Revenue & Profit
For these problems,
will represent the number of items and
will represent the money.
The fixed costs for a certain item are $140 per week. The cost to produce each item is $8 per item.
Using this information, what is the cost equation? Give your answer in slope-intercept form:
The retailer intends to sell each item for $21/item.
Using this information, what is the revenue equation? Give your answer in slope-intercept form:
If in this week 8 items are made, and all items are sold in the week, what are the total costs to the retailer?
Cost = $
What is the revenue from selling 8 items?
Revenue = $
Finally, what is the profit for this retailer?
Profit = $
For these problems,
will represent the number of items and
will represent the money.
The fixed costs for a certain item are $140 per week. The cost to produce each item is $8 per item.
Using this information, what is the cost equation? Give your answer in slope-intercept form:
The retailer intends to sell each item for $21/item.
Using this information, what is the revenue equation? Give your answer in slope-intercept form:
If in this week 8 items are made, and all items are sold in the week, what are the total costs to the retailer?
Cost = $
What is the revenue from selling 8 items?
Revenue = $
Finally, what is the profit for this retailer?
Profit = $
Answers
GPT-4o mini
To solve this problem, we will first derive the cost and revenue equations based on the given information.
### 1. Cost Equation
The total cost includes fixed costs plus the variable costs of producing the items. The fixed cost is $140 per week, and the variable cost to produce each item is $8.
Let \( C \) represent the total cost and \( x \) represent the number of items produced.
The cost equation in slope-intercept form is:
\[
C = 8x + 140
\]
### 2. Revenue Equation
The revenue is generated from selling items. If the retailer sells each item for $21, then the revenue generated by selling \( x \) items can be represented as:
Let \( R \) represent total revenue.
The revenue equation in slope-intercept form is:
\[
R = 21x
\]
### 3. Total Costs for 8 Items
Now we can calculate the total costs if 8 items are produced:
\[
C = 8(8) + 140 = 64 + 140 = 204
\]
Thus, the total costs to the retailer are:
\[
\text{Cost} = \$204
\]
### 4. Total Revenue from Selling 8 Items
Now we can calculate the total revenue from selling 8 items:
\[
R = 21(8) = 168
\]
Thus, the revenue from selling 8 items is:
\[
\text{Revenue} = \$168
\]
### 5. Profit Calculation
Profit is calculated as total revenue minus total costs:
\[
\text{Profit} = R - C = 168 - 204 = -36
\]
Thus, the profit for the retailer, in this case, is:
\[
\text{Profit} = -\$36
\]
### Summary:
- Cost equation: \( C = 8x + 140 \)
- Revenue equation: \( R = 21x \)
- Total costs for 8 items: \$204
- Total revenue from selling 8 items: \$168
- Profit for the retailer: -\$36
### 1. Cost Equation
The total cost includes fixed costs plus the variable costs of producing the items. The fixed cost is $140 per week, and the variable cost to produce each item is $8.
Let \( C \) represent the total cost and \( x \) represent the number of items produced.
The cost equation in slope-intercept form is:
\[
C = 8x + 140
\]
### 2. Revenue Equation
The revenue is generated from selling items. If the retailer sells each item for $21, then the revenue generated by selling \( x \) items can be represented as:
Let \( R \) represent total revenue.
The revenue equation in slope-intercept form is:
\[
R = 21x
\]
### 3. Total Costs for 8 Items
Now we can calculate the total costs if 8 items are produced:
\[
C = 8(8) + 140 = 64 + 140 = 204
\]
Thus, the total costs to the retailer are:
\[
\text{Cost} = \$204
\]
### 4. Total Revenue from Selling 8 Items
Now we can calculate the total revenue from selling 8 items:
\[
R = 21(8) = 168
\]
Thus, the revenue from selling 8 items is:
\[
\text{Revenue} = \$168
\]
### 5. Profit Calculation
Profit is calculated as total revenue minus total costs:
\[
\text{Profit} = R - C = 168 - 204 = -36
\]
Thus, the profit for the retailer, in this case, is:
\[
\text{Profit} = -\$36
\]
### Summary:
- Cost equation: \( C = 8x + 140 \)
- Revenue equation: \( R = 21x \)
- Total costs for 8 items: \$204
- Total revenue from selling 8 items: \$168
- Profit for the retailer: -\$36