Find the optimal solution for the following problem. (Round your answers to 3 decimal places.)Maximize C = 9x + 7ysubject to 8x + 10y ≤ 1711x + 12y ≤ 25and x ≥ 0, y ≥ 0.1. what is the optimal value of x?2. What is the optimal value of y?3. What is the maximum value of the objective function?

Answer: Maximize C =[tex]9x + 7y[/tex] [tex]8x + 10y \leq 17[/tex][tex]11x + 12y\leq 25[/tex]and x ≥ 0, y ≥ 0Plot the lines on graph [tex]8x + 10y \leq 17[/tex][tex]11x + 12y\leq 25[/tex][tex]x\geq 0[/tex][tex]y\geq 0[/tex]So, boundary points of feasible region are (0,1.7) , (2.125,0) and (0,0)Substitute the points in  Maximize CAt  (0,1.7) Maximize C =[tex]9(0) + 7(1.7)[/tex] Maximize C =[tex]11.9[/tex]At  (2.125,0) Maximize C =[tex]9(2.125) + 7(0)[/tex] Maximize C =[tex]19.125[/tex]At   (0,0) Maximize C =[tex]9(0) + 7(0)[/tex] Maximize C =[tex]0[/tex]So, Maximum value is attained at   (2.125,0) So, the optimal value of x is 2.125The optimal value of y is 0The maximum value of the objective function is 19.125