for any work involving matrices, could you draw them out for me to visualize please? It would be much appreciated.

1. Consider the following set of four linear inequalities:

A: x + y + z > 3

B: 2x - y + 10z < 11

C: 5x + 5z > 10

D: 2y - z > 0

For each of the following points, which constraints are active? Which constraints are not active but satisfied?

1. (1, 1, 1)
2. (0, 1, 2)
3. (3, 1, -1)

2. For the following linear program, specify the A matrix and x, b, and c vectors.

Min a + 4b + 3c + 7d - 2e

St 2a + 6b + 2d = 2

2b - d + 2e = 1

b + 3c + 4d = 1

a, b, c, d, e > 0

a) Find all basic feasible solutions to this problem. Be sure to show all the work.

3. Consider the following linear program:

Min x - y - 2z

St x + 4y + 3z = 9

x > 2

z > 2

x, y, z > 0

a) Convert to the following standard form and use the results for the remaining sections in this problem:

Ax = b

x > 0

b)Specify the A matrix and x, b, and c vectors.

c)Find all basic feasible solutions to this problem

d)Find the objective value for each of these BFS's.

e)Which one is the best?

f) BONUS: Do you think this solution is optimal? Why or why not?