A cost is fixed if it does not change in response to change in the level of activity and variable if the total cost changes per unit of activity. Total variable costs increase or decrease in direct proportion to the activity level. The total costs of production are made up of fixed and variable costs.

The linear cost function is a straight-line cost function that can be shown as y = a + bx

y is the total cost to be predicted, a is a constant (fixed cost) and b is the cost that will be the same for eact unit of activity and x is the number of units of actibity.

The relevant range of activity is the levels of activity that the firm has experiences in past periods. In this range it is assumed that the relationship between independent and dependent variables will be similar.

Cost-volume-profit (CVP) analysis is a technique to assist them making decisions by examining the relationships between cost, volume and profit. Break even is a point in CVP analusis where costs are equal to revenues. The contribution margin is the sales revenue less all variable costs. Provided that variable costs are less then sales revenue, then ethere is a contribution to reducing the cost of fixed overheads.

P = Sx - (FC + VCx) or Sx = VCx + FC + P

P = expected profit, S = selling price per unit, x = number of units sold, FC = Fixed Cost, VC = Variable Cost

CVP analysis is limited by the assumption that costs and revenues are limited. It assumes a single-product firm. Not all costs are fixed or variable, some can be mixed. In a multi-product firm, fixed costs may be difficult to allocate.