Question

In a business, a cost function describes the total cost associated with a given level of production. A revenue function describes the amount of money received at a given level of production. These two functions form a system of equations. The solution of this system is called the break-even point. It is the level of production for which revenue equals cost. Business is profitable only if revenue is greater than the cost. Suppose the system of equations containing the revenue and the cost functions is an inconsistent system. What does this mean in the context of businesses?

a. The business will sell a lot of products.
b. The business will sell products for a very high price.
c. The business will never profit.
d. The business will make lots of products.

Answer 1

An inconsistent system of cost and revenue functions means that no break-even point exists, and thus the business will never profit as the cost always exceeds the revenue.

Step-by-step explanation:

When the system of equations containing the revenue and the cost functions is an inconsistent system, it implies that there is no level of production at which the total cost and total revenue are equal. Therefore, no break-even point exists for the business. In practical terms, this means that the business will never profit (option c), because the total revenue is always less than the total cost at any level of production, indicating that the business would incur losses irrespective of how many units are sold.