A product will produce a profit only when the revenue R from...

A product will produce a profit only when the revenue R from selling the product exceeds the cost C of producing it. In Exercises 69 and 70, find the least whole number of units x that must be sold for the business to show a profit for the item described. Speedy Delivery finds the cost of making $x$ deliveries is $C=3 x+2300,$ while the revenue produced from them is $R=5.50 x(C \text { and } R$ in dollars).

A product will produce a profit only when the revenue R from selling the product exceeds the
cost C of producing it. In Exercises 69 and 70, find the least whole number of units x that must
be sold for the business to show a profit for the item described.
Speedy Delivery finds the cost of making $x$ deliveries is $C=3 x+2300,$ while the revenue produced from them is $R=5.50 x(C \text { and } R$ in dollars).

Key Concepts

Inequality Solving

Inequality solving is the process of finding the range of values that satisfy a given inequality. In the context of profit analysis, it involves determining the minimum number of units that must be sold for revenue to exceed costs. This skill is important in many areas of mathematics and business as it helps in decision-making and optimizing performance.

Break-Even Analysis

Break-even analysis identifies the point at which total revenue equals total cost, meaning that there is no profit or loss. Determining the break-even point is crucial for businesses to understand how many units need to be sold before making a profit, and it provides a basis for making pricing and production decisions.

Cost Function

A cost function expresses the total cost incurred in producing a given number of units. It typically includes fixed costs that do not change with production volume and variable costs that vary with the number of units produced. Understanding the cost function is essential for budgeting and setting sales targets.

Revenue Function

A revenue function represents the total income generated by selling a certain number of units of a product, where the function relates the number of units sold to the income received. This function is central to analyzing business performance, as it helps determine whether the income generated will cover the costs and yield a profit.

Transcript

Please give Ace some feedback