1a.A company's daily profit, P(x) is given by P(x) = -2x² + (200 - 4*25)x + 2*25² - 200*25 + 5500, where x is the number of articles produced per day. (ATTN: in this problem and the problems below, checkat least twice all calculated(in accord with the PEMDAS rule!) numeric coefficients and constants that depend onN before you'll proceed with a solution!) Use the calculus technologyto find the value x_opt so that the daily profit is a maximum.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 P(x)). See the precalculus file 24_Handout_9_QUADRATIC FUNCTIONS.doc. Round off the value x_opt to nearest integer). Evaluate the maximum value P(x_opt) of the function P(x).