## 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?

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