Consider the three-dimensional linear optimization problem


maximize x1 + x2 + x3

subject to x1 + 2x2 + 2x3 ≤ 20

2x1 + x2 + 2x3 ≤ 20

2x1 + 2x2 + x3 ≤ 20

x1 ≥ 0 x2 ≥ 0 x3 ≥ 0


Required:

a. List all basic solutions.

b. List all basic feasible solutions.

c. Compute the value of the objective function at each basic feasible solution.

d. Solve the linear optimization problem. Find the optimal objective and list any and every optimal basic feasible solution