Find the optimal solution for the following problemMinimize C = 13x + 3ysubject to 12x + 14y ≥ 2115x + 20y ≥ 37and x ≥ 0, y ≥ 0.1. What is the optimal value of x?2. What is the optimal value of y?3.What is the minimum value of the objective function?

Answer:1. optimal value of x, is 02. optimal value of y, is 37/203. optimal value of objetive function, is 111/20Step-by-step explanation:In the graphic of the attached file you can see the feasible region for the linear programming problem.The vertices of this region are the origin and the intercepts of the line 1[tex]5x + 20y = 37[/tex]. That is, [tex]A (0, 37/20)[/tex] and [tex]B (37/15, 0)[/tex]. According to the optimality theorem, the optimal solution of the problem must be reached at one of the vertices of the feasible region, therefore,We evaluate the objective function [tex]Z = 13x + 3y[/tex] at each vertex:[tex]Z (0, 37/20) = 13 (0) + 3 (37/20) = 111/20\\\\Z (37/15, 0) = 13 (37/15) + 3 (0) = 481/215[/tex]Since [tex]Z (0, 37/20)[/tex] is less than [tex]Z (37/15, 0)[/tex], then the optimal solution is reached at [tex]x = 0[/tex], [tex]y = 37/20[/tex].optimal value of x, is 0optimal value of y, is 37/20optimal value of objetive function, is 111/20