Teknik Riset Operation

Soal TRO Set 3.3B
1. This problem is designed to reinforce your understanding of the simplex feasibility condition. In the first tableau in Example 3.3-1, we used the minimum (nonnegative) ratio test to determine the leaving variable. Such a condition guatantees that none of the new values of the basic variables will become negative ( as stipulated by the definition of the LP). To demonstrate this point, force S2 , insteas of S1 , to leave the basic solution. Now, look at the resulting simplex tableau , and you will note that S1 assumes a negative value ( = - 12 ), meaning that the new solution is infeasible. This situation will never occur if we employ the minimum – ratio feasibility condition.
2. Consider the following set of constraints :
X1 + 2x2 + 2x3 + 4x4 ≤ 40
2x1 – x2 + x3 +2x4 ≤ 8
4x1 – 2x2 + x3 – x4 ≤ 10
x1, x2, x3, x4 ≥ 0
solve the problem for each of the following objective functions
a. Maximize Z = 2x1 + x2 – 3x3 + 5x5
b. Maximize Z = 8x1 + 6x2 +3x3 – 2x4
c. Maximize Z = 3x1 – x2 + 3x3 + 4x4
d. Maximize Z = 5x1 – 4x2 + 6x3 – 8x4