Consider the following LP problem:
Maximize Z = 40X1 + 30X2 + 60X3
Subject to: 1X1 + 1X2 + 1X3 => 90
12X1 + 8X2 + 10X3 =< 1500
X1, X2, X3 => 0
How many slack, surplus, and artificial variables would be necessary if the simplex method were used to solve this problem?
a. 3 slack, 3 surplus, and 3 artificial
b. 1 slack, 2 surplus, and 2 artificial
c. 1 slack, 4 surplus, and 4 artificial
d. 1 slack, 1 surplus, and 1 artificial
e. none of the above.