To produce its most popular skateboard, Top Dog Boards has a...

To produce its most popular skateboard, Top Dog Boards has a fixed cost in its factory of $\$ 5800$ plus a cost of $\$ 6.20$ for each skateboard built. The cost of production during the month of October was $\$ 11,008$. How many skateboards were produced?

Key Concepts

Cost Function

The cost function is an equation that represents the total cost of production as a function of the number of units produced. It includes both fixed costs and variable costs, typically expressed as a constant term plus a term that multiplies the unit variable cost by the quantity produced. This function helps businesses determine total expenditures based on different output levels.

Fixed Cost

A fixed cost is an expense that does not change with the level of production or sales. It remains constant regardless of how many units are produced, meaning that even if production is zero, the fixed cost still needs to be paid. This concept is essential in business and economics because it represents the base level cost before any variable costs are added.

Variable Cost

A variable cost changes directly in proportion to the number of units produced. As production increases, variable costs increase at a constant rate per unit. This concept is important when calculating total production costs, as it allows for analysis of marginal costs and helps in making decisions about scaling production.

Linear Equation

A linear equation is an algebraic expression that describes a straight-line relationship between variables. In cost analysis, the fixed and variable costs combine to form a linear equation where the total cost is equal to the fixed cost plus the product of the variable cost per unit and the number of units. This form is useful for solving problems where one needs to find the unknown quantity produced given a total cost.

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