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?
Expand 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
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