Solve each of these problems by computer and obtain the optimal values of the decision variables and the objective function.

a. Maximize Z = 4x1 + 2x2 + 5x3 Subject to:

1 x 1  + 2 x 2  + 1 x 3

≤

25 1 x 1  + 4 x 2  + 2 x 3 ≤ 40 3 x 1  + 3 x 2  + 1 x 3 ≤ 30 x 1 , x 2 , x 3

≥

0

b. Maximize Z = 10x1 + 6x2 + 3x3 Subject to:

1 x 1  + 1 x 2  + 2 x 3

≤

25 2 x 1  + 1 x 2  + 4 x 3 ≤ 40 1 x 1  + 2 x 2  + 3 x 3 ≤ 40 x 1 , x 2 , x 3

≥

0 LO.1