The profit (P) in dollars for a company is modeled by the function P(x) P(x)= -750x^2+15,000x where x is the number of the items produced
To find the maximum profit, we need to determine the value of x that corresponds to the vertex of the quadratic function representing the profit. The vertex of a quadratic function is given by the formula x = -b / (2a), where a and b are the coefficients in the quadratic equation.
In this case, the profit function is P(x) = -750x^2 + 15,000x, so we have a = -750 and b = 15,000. By substituting these values into the vertex formula, we can find the value of x that yields the maximum profit.
x = -b / (2a)
x = -15,000 / (2 * -750)
x = -15,000 / -1,500
x = 10
Therefore, the company will achieve maximum profit when it produces 10 items.