Table 10-2
Maximize Z = 34 X 1 + 43 X 2 + 29 X 3
Subject to: 5 X 1 + 4 X 2 + 7 X 3 ≤ 50
1 X 1 + 2 X 2 + 2 X 3 ≤ 16
3 X 1 + 4 X 2 + 1 X 3 ≤ 9
all X i are integer and non-negative
Final Integer Solution: Z = 208
Decision
Variable Solution
X 1 1
X 2 0
X 3 6
-According to Table 10-2,which presents a solution for an integer programming problem,at the optimal solution,how much slack exists in the third constraint?
A)0
B)9
C)5
D)6
E)-1

Question

Table 10-2
Maximize Z = 34 X 1 + 43 X 2 + 29 X 3 
Subject to: 5 X 1 + 4 X 2 + 7 X 3 ≤ 50
1 X 1 + 2 X 2 + 2 X 3 ≤ 16
3 X 1 + 4 X 2 + 1 X 3 ≤ 9
all X i are integer and non-negative
Final Integer Solution: Z = 208
Decision
Variable Solution
X 1 1
X 2 0
X 3 6
-According to Table 10-2,which presents a solution for an integer programming problem,at the optimal solution,how much slack exists in the third constraint?
A)0
B)9
C)5
D)6
E)-1

Quizplus · Accepted Answer

The third constraint is 3 XS1U1B11S1U1B0 + 4 XS1U1B12S1U1B0 + 1 XS1U1B13S1U1B0 ≤ 9. At the optimal solution, XS1U1B11S1U1B0 = 1, XS1U1B12S1U1B0 = 0, and XS1U1B13S1U1B0 = 6. Plugging these values into the constraint, we get 3(1) + 4(0) + 1(6) = 9. Therefore, the slack in the third constraint is 9 - 9 = 0.

Table 10-2 Maximize Z = 34 X1 + 43 X2 + 29

Table 10-2 Maximize Z = 34 X₁ + 43 X₂ + 29