A woman decides to start a small business making monogrammed...

A woman decides to start a small business making monogrammed cocktail napkins. She can set aside $\$ 1870$ for monthly costs. Fixed costs are $\$ 1329.50$ per month and variable costs are $\$ 3.70$ per set of napkins. How many sets of napkins can she afford to make per month?

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Key Concepts

Inequalities and Solving Linear Equations

Solving problems with a budget constraint typically involves setting up and solving linear equations or inequalities. This process includes isolating the variable (often representing the number of units) to determine maximum production possibilities within the budget.

Budget Constraint

A budget constraint represents the limit on spending or investment based on available resources. In cost problems, it requires that the total costs do not exceed a set budget, leading to an inequality that must be satisfied.

Fixed Costs

Fixed costs refer to expenses that remain constant regardless of the level of production or output. In business, these are costs that must be paid even if nothing is produced, such as rent or monthly subscriptions.

Variable Costs

Variable costs change in direct proportion to the level of production. They include expenses that increase as more units are produced, such as materials or labor directly related to each unit.

Total Cost Equation

The total cost equation sums the fixed costs and the product of the variable cost per unit and the number of units produced. This forms the basis for understanding how overall costs change with production volume.

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