## Break-Even

The cost of producing a product from a machine shop is: C=$10,000 + (0.05)(P), where P is the number of products produced. If the items sell for $4.50 each, how many items must be produced to break even?

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__**Hint**

**Hint**

Break even implies
$$Earnings=Cost$$

Break even implies
$$Earnings=Cost$$

$$$C=10,000+0.05\cdot P$$$

$$$4.5P=10,000+0.05P$$$

Solve for P:

$$$4.5P-0.05P=10,000$$$

$$$4.45P=10,000$$$

$$$P=\frac{10,000}{4.45}=2,247.19$$$

The factory must produce 2,248 units to break even.

2,248 units