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: y=



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: y=



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 = $

Answer 1

To solve this problem, let's break down each component step by step.

**1. Cost Equation:**

The total cost \( C \) can be broken into fixed costs and variable costs.

- **Fixed costs**: $140 per week
- **Variable costs**: $8 per item produced

The cost equation can be formulated as:
\[ C = \text{Fixed costs} + \text{Variable cost per item} \times \text{number of items} \]
\[ C = 140 + 8x \]
where \( C \) represents the total cost and \( x \) represents the number of items.

Thus, the cost equation in slope-intercept form is:
\[ C = 8x + 140 \]

**2. Revenue Equation:**

The total revenue \( R \) from selling \( x \) items at $21 per item can be described as:
\[ R = \text{Price per item} \times \text{number of items} \]
\[ R = 21x \]

Thus, the revenue equation in slope-intercept form is:
\[ R = 21x \]

**3. Total Costs for 8 Items:**

Now, if 8 items are made:
\[ C = 140 + 8(8) \]
\[ C = 140 + 64 \]
\[ C = 204 \]

So, the total costs to the retailer for 8 items is:
\[ \text{Cost} = \$204 \]

**4. Revenue from Selling 8 Items:**

For 8 items sold at $21 each:
\[ R = 21(8) \]
\[ R = 168 \]

So, the revenue from selling 8 items is:
\[ \text{Revenue} = \$168 \]

**5. Profit for the Retailer:**

Profit \( P \) is calculated as the difference between revenue and costs:
\[ P = R - C \]
Substituting the values we calculated:
\[ P = 168 - 204 \]
\[ P = -36 \]

Thus, the profit for the retailer is:
\[ \text{Profit} = -\$36 \]

### Summary of Answers:
- **Cost Equation**:
\[ C = 8x + 140 \]

- **Revenue Equation**:
\[ R = 21x \]

- **Total Costs for 8 Items**:
\[ \text{Cost} = \$204 \]

- **Revenue from Selling 8 Items**:
\[ \text{Revenue} = \$168 \]

- **Profit for the Retailer**:
\[ \text{Profit} = -\$36 \]