A snow cone vendor on the Virginia Beach boardwalk has...

A snow cone vendor on the Virginia Beach boardwalk has several costs of doing business. She pays salaries of $\$ 2000$ per month and other fixed costs, such as utilities and kiosk rental, of $\$ 1150$ per month. Each snow cone sold costs her 36 cents. a. Write an equation for the total cost of selling snow cones for a month depending on the number of snow cones sold. b. What will the monthly cost be if she sells 3000 snow cones in a month? c. How many snow cones can she sell if the total monthly cost cannot exceed a budget of $\$ 4400 ?$

A snow cone vendor on the Virginia Beach boardwalk has several costs of doing business. She pays salaries of $\$ 2000$ per month and other fixed costs, such as utilities and kiosk rental, of $\$ 1150$ per month. Each snow cone sold costs her 36 cents.
a. Write an equation for the total cost of selling snow cones for a month depending on the number of snow cones sold.
b. What will the monthly cost be if she sells 3000 snow cones in a month?
c. How many snow cones can she sell if the total monthly cost cannot exceed a budget of $\$ 4400 ?$

Key Concepts

Linear Functions

A linear function describes a relationship between two variables where the rate of change is constant. This concept is fundamental in representing real-world scenarios such as costs or revenues that change uniformly with respect to the number of items produced or sold.

Fixed and Variable Costs

Fixed costs are expenses that remain constant regardless of the number of goods produced, while variable costs change in proportion to the production volume. Understanding the distinction between fixed and variable costs is essential in developing models, like cost functions, that accurately reflect total expenses in business activities.

Cost Function

A cost function combines both fixed and variable costs into a single equation that computes the total cost for a given level of production or sales. This function is often linear, reflecting the addition of a constant fixed cost and a variable cost multiplied by the number of items.

Solving Linear Equations

Solving linear equations involves manipulating the equation to isolate the unknown variable, allowing one to find the specific values that satisfy the equality. This process is a critical step in determining specific outputs or budgeting thresholds in economic contexts.

Solving Linear Inequalities

Solving linear inequalities is similar to solving linear equations, but instead of finding a single solution, it identifies a range of values that meet the specified condition. This method is particularly useful in situations such as budgeting, where there is a maximum allowable value that must not be exceeded.

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