A manufacturer is in the business of producing small car models. He finds that the daily cost in dollars, C(x), of producing x models is given by the quadratic function

C(x) = x² - (120 + 2*25)x + 25² + 122*25 + 4300. Use the calculus technology to find the level x_opt of production that will minimize such a cost function. To verify your result, use the corresponding non-calculus technology (the point x_opt is x-coordinate of the vertex of parabola representing the function C(x)). Round off the value x_opt to nearest integer). Evaluate the minimum value C(x_opt) of the function