Question

For a certain business, the revenue at least equals the total cost, given by the equation 60x≥35x+500. What does this inequality represent in terms of business operations?

Answer 1

The inequality 60x≥35x+500 shows the break-even point for a business, where total revenues at least equal total costs. Business operations aim for total revenues to exceed total costs to make a profit. The goal is to find the quantity of output that maximizes profit, where revenue minus cost is the greatest.

Step-by-step explanation:

The inequality 60x≥35x+500 represents the condition in business operations where total revenue is at least equal to total cost. The term 60x refers to the total revenue that the business makes from selling products or services, where 'x' is the number of units sold and '60' represents the revenue per unit. Conversely, 35x+500 represents the total costs incurred by the business, with '35x' being the variable costs depending on the number of units produced, and '500' being the fixed costs that do not change with the level of production.For the business to break even or be profitable, it must sell a quantity of products such that revenues cover all costs. A business experiences losses when costs exceed revenues, as illustrated in the example where producing five units results in total costs of $130 and total revenues of only $125, hence a loss of $5. To achieve maximum profit, the business must produce and sell at a quantity where the difference between total revenue and total cost is the greatest.