Question

Acme Innovations makes and sells lamps. Their profit, P, in hundreds of dollars earned, is a function of the number of lamps sold in thousands.

From historical data, they know that their company's profit is modeled by the function
P(x) = -x + 11x2 - 4x - 60.
How many lamps should the company make in order to make a profit?

Answer 1

The student's question involves using algebra to find out how many thousands of lamps Acme Innovations must sell to make a profit, by identifying where the profit function P(x) = -x² + 11x - 60 is greater than zero.

Step-by-step explanation:

The question is related to finding the quantity of lamps Acme Innovations needs to produce to earn a profit. The profit function is given by P(x) = -x² + 11x - 60, where x is in thousands of lamps and P(x) is in hundreds of dollars. To determine the number of lamps that need to be sold to make a profit, we need to find the values of x for which P(x) is greater than zero.

This involves finding the roots of the quadratic equation and determining the range for which the profit function is positive. Once the function's graph is sketched, you can visually identify the positive regions of the profit function.