Math 107 - Chapter 3.3 Linear Models and Business Applications

Vocabulary flashcards covering linear function applications including cost, revenue, profit, marginal analysis, linear depreciation, break-even analysis, and supply and demand models.

Linear Function

A function in which all variable exponents are 0 or 1, producing a straight line when graphed and used to model real-world applications.

Fixed Costs

The costs incurred by a business regardless of production volume, calculated as $C(0)$ in a cost function.

Variable Costs

The costs directly associated with producing each additional unit, represented by the slope $c$ in a linear cost model $C(x) = cx + F$ or calculated as $\frac{C(x) - C(0)}{x}$.

Average Cost per Unit

The total cost of production divided evenly across all units produced, defined mathematically as $\overline{C}(x) = \frac{C(x)}{x}$.

Marginal Cost

The rate of change of total cost with respect to output quantity (equal to the slope for linear models), representing the cost of producing one additional unit.

Marginal Revenue

The rate of change of total revenue with respect to sales quantity, representing the extra revenue gained by selling one additional unit.

Marginal Profit

The rate of change of total profit with respect to quantity, representing the additional profit earned by producing and selling one extra unit.

Linear Depreciation

An accounting procedure where an asset's book value decreases by a constant dollar amount every year over its useful life until reaching a value of $0$.

Break-Even Point

The level of production $x$ at which total revenue equals total cost ($R(x) = C(x)$), resulting in a profit of zero ($P(x) = 0$).

Market Equilibrium

The economic state where quantity supplied matches quantity demanded ($q_s = q_d$), found at the point where the supply and demand curves intersect.

Surplus

A condition in the market at a given price where quantity demanded is less than quantity supplied ($q_d < q_s$), indicating excess production.

Shortage

A condition in the market at a given price where quantity demanded is greater than quantity supplied ($q_d > q_s$), indicating insufficient production.