The corner points of the feasible region determined by a system of linear constraints are (0, 10), (5, 5), (15, 15), and (0, 20). Let Z = ax + by, where a, b > 0. The condition on a and b so that the maximum value of Z occurs at both points (15, 15) and (0, 20) is:

Consider the linear programming problem: Maximize 3x1 + 4x2 subject to: 3x1 + 2x2 ≤ 12, 3x1 + 5x2 ≤ 15, 2x1 - x2 ≥ 0, x2 ≤ 2, and x1, x2 ≥ 0. Which of the following values is the optimal value of the objective function in the feasible region?

Consider the following Linear Programming Problem (LPP): Maximize: Z = 4x + 2y Subject to: 2x + y ≤ 8 x + y ≤ 5 x ≥ 0, y ≥ 0 Which of the following statements is true regarding this problem?