Profit The revenue for selling x units of a product is...

Profit The revenue for selling $x$ units of a product is $R=115.95 x,$ and the cost of producing $x$ units is
$C=95 x+750 .$ To obtain a profit, the revenue must be greater than the cost. For what values of $x$ will this product return a profit?

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Key Concepts

Inequalities

Inequalities are mathematical expressions used to compare values, and in this context, they help determine when the revenue exceeds the cost. Solving an inequality such as Revenue > Cost enables one to find the minimum number of units that need to be sold to achieve a profit, a key step in decision-making processes in business.

Profit Function

The profit function is defined as the difference between the revenue function and the cost function, given by Profit(x) = Revenue(x) - Cost(x). This function indicates the financial gain or loss at different levels of production, and understanding it is crucial for assessing business performance.

Revenue Function

The revenue function represents the total income generated from selling products or services. It is generally expressed as a function of the number of units sold, often taking the form R(x) = price per unit × number of units, which helps in understanding how sales volume affects income.

Cost Function

The cost function represents the total production costs, comprising both variable costs (which change with the number of units produced) and fixed costs (which remain constant regardless of production level). It is typically expressed as C(x) = variable cost per unit × number of units + fixed cost, helping to determine the breaking point for profitability.

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