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Understanding Revenue, Cost, and Profit Functions in Business Economics

This guide explains the relationship between revenue, cost, and profit functions for a company producing motorbikes. It details how to formulate these functions based on fixed and variable costs, using a practical example. A company incurs a fixed cost of $14,000 and a production cost of $1,900 per motorbike, while selling each for $2,400. We derive the cost function, revenue function, and profit function. Additionally, we determine the number of units needed to sell in order to achieve profit, illustrating that more than 28 motorbikes must be sold to become profitable.

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Understanding Revenue, Cost, and Profit Functions in Business Economics

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    16. Revenue and Cost Functions A company produces and sells x units of a product. Revenue Function R(x) = (price per unit sold)x Cost Function C(x) = fixed cost + (cost per unit produced)x

    17. The Profit Function The profit, P(x), generated after producing and selling x units of a product is given by the profit function P(x) = R(x) C(x) where R and C are the revenue and cost functions, respectively.

    18. Business Application EXAMPLE A company that manufactures motorbikes has a fixed cost of $14,000. It costs $1900 to produce each motorbike. The selling price per motorbike is $2400. Write the cost function, the revenue function and the profit function. Determine how many bikes must be produced and sold to have a profit. Cost Function: C(x) = 14,000 + 1900x

    19. Business Application Revenue Function: R(x) = 2400x Profit Function: P(x) = R(x) C(x) = 2400x (14,000 + 1900x) = 2400x 14,000 - 1900x = 500x 14,000

    20. Business Application How many must be sold to make a profit? P(x) = 500x 14,000 A profit occurs when P(x) > 0 500x 14,000 > 0 500x > 14,000 x > 28 More than 28 motorbikes must be produced and sold to make a profit.

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