Question

The profit for a product is given by ​p(x)=−11x2 1430x−44,000​, where x is the number of units produced and sold. how many units give break even​ (that is, give zero​ profit) for this​ product?

Answer 1

To determine the break-even point, the profit function p(x) = -11x^2 + 1430x - 44,000 needs to be set to zero and solved for x, which will provide the number of units that must be produced and sold for zero profit.

Step-by-step explanation:

The question is asking how many units must be produced and sold for the product to break even, which means to have a zero profit. To determine this, we need to set the profit function p(x) = -11x^2 + 1430x - 44,000 equal to zero and solve for x. Breaking even occurs when total revenue equals total cost, resulting in zero profit.

We will solve the quadratic equation 0 = -11x^2 + 1430x - 44,000 to find the values of x that represent the break-even points. This may result in two possible values for x, as a quadratic equation can have up to two real solutions. The positive value (if any) from these solutions will be the number of units that need to be produced and sold to break even.