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A linear cost model

A linear model fits when something increases by a fixed amount per unit. The cost can be a fixed amount plus a fixed price per unit. The slope is the price per unit, and the constant term is the cost when the number of units is zero. The graph is a straight line. A fixed percentage growth is exponential instead, so you must see whether the increase is a fixed amount or a fixed percentage.

C(x)=ax+bC(x) = ax + blinear cost
a=C(x2)−C(x1)x2−x1a = \frac{C(x_2) - C(x_1)}{x_2 - x_1}slope

Symbols

aaprice per unitNOK
bbfixed costNOK
xxnumber of units

Example

C(x)=5000+40xC(x) = 5000 + 40x. Ten units cost 5000+40⋅10=54005000 + 40 \cdot 10 = 5400 NOK.

Each new unit costs 40 NOK more.

A fixed addition gives a straight line. A fixed percentage gives a curved graph.
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Part of Mathematics S1: Functions and models.