Question

A company’s profit is modeled by the function p(x) = -2x2 + 60x − 2, where p is the profit in thousands of dollars and x is the number of units sold in hundreds. 
Based on the profit function, the company has to make ___ hundred units to make a maximum profit

Answer 1

Note:  Please write "x^2" (not 'x2') to indicate "the square of x."

p(x) = -2x2 + 60x − 2 is a quadratic function whose graph is that of an inverted parabola.  The vertex (which here represents the largest p(x) value) can be found using the formula 

x  = -b / (2a), which comes out to   x = -60 / (2*-2) = 15.

The company has to make 15 hundred units to gain maximum profit.