Quest Manufacturing is building a product that costs $200 to start to build and $6.40 per unit sold.  The company plans to sell each unit for $10.50.  The company wrote an inequality to determine the minimum number of units (u) that it needs to sell to break even or make a profit on the product.10.50u greater than or equal to 200+6.40u
 What is the minimum amount of units that the company needs to sell to break even or make a profit on the product?

We are given the inequality:

\[
10.50u \geq 200 + 6.40u
\]

Where:
- $u$ is the number of units sold.
- $200 is the fixed cost to start building.
- $6.40 is the cost per unit sold.
- $10.50 is the selling price per unit.

The goal is to solve this inequality for $u$, which represents the minimum number of units needed to break even or make a profit.

### Step 1: Subtract $6.40u$ from both sides

\[
10.50u - 6.40u \geq 200
\]

\[
4.10u \geq 200
\]

### Step 2: Divide both sides by 4.10

\[
u \geq \frac{200}{4.10}
\]

\[
u \geq 48.78
\]

Since the company cannot sell a fraction of a unit, it must sell at least **49 units** to break even or make a profit.

### Final Answer: 
The company must sell at least **49 units** to break even or make a profit.

Do you want details or have any questions?

Here are 5 related questions you can explore:
1. How much profit will the company make if they sell 60 units?
2. What if the cost per unit increases to $7.00, how many units would they need to sell?
3. What happens if the starting cost decreases to $150? How many units are needed then?
4. How would the inequality change if the selling price per unit drops to $9.50?
5. How much revenue will the company generate after selling 100 units?

**Tip:** Always isolate the variable on one side of the inequality or equation to simplify solving.

Quest Manufacturing is building a product that costs $200 to start to build and $6.40 per unit sold. The company plans to sell each unit for $10.50. The company wrote an inequality to determine the minimum number of units (u) that it needs to sell to break even or make a profit on the product. 10.50u greater than or equal to 200+6.40u. What is the minimum amount of units that the company needs to sell to break even or make a profit on the product?

Determine the minimum number of units Quest Manufacturing needs to sell to break even or make a profit. The problem involves solving the inequality 10.50u ≥ 200 + 6.40u, where $200 is the fixed startup cost, $6.40 is the per-unit cost, and $10.50 is the selling price per unit. Learn the steps to find that the company must sell at least 49 units to break even.

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