The intercept as fixed cost in a production line

Question

A small workshop models its daily production cost against the number of units it makes:

$\widehat{\text{cost}} = 500 + 12 \cdot (\text{units produced}).$

What is the predicted cost of a day with zero units made, and what real-world quantity does that intercept represent?

Accepted Answer

Set the input to zero units: \widehat{	ext{cost}} = 500 + 12 	imes 0 = 500 	ext{ dollars.} The intercept \500 is the predicted cost of a day that produces nothing. That has a clean business meaning: it is the fixed cost, the money spent no matter what, such as rent, salaried staff, and machine leases. The slope \12 is then the variable cost, the extra money each additional unit adds (materials, power). This intercept is meaningful because a zero-output day is entirely realistic (a holiday, a breakdown) and the fixed costs really are still paid. Splitting cost into a fixed part (intercept) …

The intercept as fixed cost in a production line

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