Question The manufacturer of widgets spends $5 to make each widget and sells them for $8. The manufacturer also has fixed costs each month of $1200. Find the number of widgets, x, that the manufacturer needs to sell in order to break-even. Provide your answer below:

ENGR.ECONOMIC ANALYSIS
14th Edition
ISBN:9780190931919
Author:NEWNAN
Publisher:NEWNAN
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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**Question**

The manufacturer of widgets spends $5 to make each widget and sells them for $8. The manufacturer also has fixed costs each month of $1200.

Find the number of widgets, \( x \), that the manufacturer needs to sell in order to break-even.

Provide your answer below:

\( x = \) [ ]

**Explanation:**

To find the break-even point, we need to determine when the total revenue equals total costs.

1. **Cost per Widget:** $5
2. **Selling Price per Widget:** $8
3. **Fixed Monthly Costs:** $1200

**Break-even Calculation:**

Let \( x \) be the number of widgets sold.

- **Total Cost:** \( 5x + 1200 \)
- **Total Revenue:** \( 8x \)

At break-even, Total Cost = Total Revenue:
\[ 5x + 1200 = 8x \]

Solve for \( x \):
\[ 1200 = 8x - 5x \]
\[ 1200 = 3x \]
\[ x = \frac{1200}{3} \]
\[ x = 400 \]

Therefore, the manufacturer needs to sell 400 widgets to break-even.
Transcribed Image Text:**Question** The manufacturer of widgets spends $5 to make each widget and sells them for $8. The manufacturer also has fixed costs each month of $1200. Find the number of widgets, \( x \), that the manufacturer needs to sell in order to break-even. Provide your answer below: \( x = \) [ ] **Explanation:** To find the break-even point, we need to determine when the total revenue equals total costs. 1. **Cost per Widget:** $5 2. **Selling Price per Widget:** $8 3. **Fixed Monthly Costs:** $1200 **Break-even Calculation:** Let \( x \) be the number of widgets sold. - **Total Cost:** \( 5x + 1200 \) - **Total Revenue:** \( 8x \) At break-even, Total Cost = Total Revenue: \[ 5x + 1200 = 8x \] Solve for \( x \): \[ 1200 = 8x - 5x \] \[ 1200 = 3x \] \[ x = \frac{1200}{3} \] \[ x = 400 \] Therefore, the manufacturer needs to sell 400 widgets to break-even.
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