a. Using the corner point solution method, find the optimal solution and the optimal value of the following linear programming problem. Determine the upper bound for the total number of corner points. Indicate the nature of the corner points, feasible or infeasible. maximizez=3x10.25x2 subject to 5x1+2x26 2 x10.5x20x13x23x10.75x1,x20 b. Assume that Constraint (1) is multiplied with a scalar cR and added as a new constraint to the problem. Consider the following linear programming problem. maximizez=3x10.25x2 subject to 5x1+2x26(5c)x1+(2c)x2(c)6x10.5x20x13x20x10.75x1,x20 Do the nature of the problem, the optimal value, the optimal solution, and the upper bound for the number of corner points change