Cost and Revenue Function

Every manufacturing business incurs two distinct kinds of cost. Variable cost covers expenses like raw material, direct labour, and packaging — it moves up or down with the level of production, rising when output rises and falling when output falls. Fixed cost, by contrast, stays the same no matter how much (or how little) is produced; a firm owes its fixed costs whether or not it sells a single unit.

Putting these together gives the cost function: if $V(x)$ is the variable cost of producing $x$ units and $k$ is the fixed cost, the total cost of producing $x$ units is

Revenue works differently — it depends on what a firm actually sells and at what price. If a company sells $x$ units at a price $p$ per unit, the revenue function is