To find the total profit (P(x)), we start by understanding the basic relationship in business mathematics: Profit is the difference between total revenue (R(x)) and total cost (C(x)). Mathematically, this is expressed as: [ P(x) = R(x) - C(x) ] Here, (x) represents the number of units sold. Step 1: Determine Total Revenue (R(x)) Total revenue is calculated by multiplying the selling price per unit (p(x)) with the number of units sold (x). If the selling price is constant, the revenue function is linear: [ R(x) = p \cdot x ] If the selling price varies with quantity, for example due to discounts, then (R(x) = x \cdot p(x)). Step 2: Determine Total Cost (C(x)) Total cost is the sum of fixed cost (F) and variable cost (V(x)). Fixed cost does not change with production level, while variable cost depends on the number of units produced: [ C(x) = F + V(x) ] Variable cost can be expressed as (v \cdot x) if