Problems:
1. Find the correct constraint
Let xij = gallons of component i used in gasoline j. Assume that we have two components and two types of gasoline. There are 8,000 gallons of component 1 available, and the demand gasoline types 1 and 2 are 11,000 and 14,000 gallons respectively. Write the supply constraint for component 1.
a) x21 + x22 8000
b) x12 + x22 8000
c) x11 + x12 8000
d) x21 + x22 8000
e) x11 + x12 8000
2. Find the Optimal Integer Solution 1
Consider the following integer linear programming problem ≥
Max Z = 3x1+2x
Subject to: 3x1+5x2≤30
4x1+2x2≤28
x1≤8
x1,x1≥0 and integer
The solution to the Linear programming relaxation is: x1 = 5.714, x2 = 2.571.
What is the optimal value of z of this integer linear programming problem?
a) 19 b) 20 c) 22 d) 24
3. Find the optimal integer solution 2
Max Z = x1+6x2
subject to : 17x1+8x2≤136
3x1+4x2≤36
x1,x1≥0 and integer
Find the optimal value of z.
a) 54 b) 55 c) 60 d) 61
4. Find the Optimal Integer Solution
Max Z = 3x1+5x2
subject to: 7x1+12x2≤136
3x1+5x2≤36
x1,x1≥0 and integer
Find the optimal value of z.
a) 30 b) 32 c) 36 d) 38
5. Integer Optimization Constraint
In a capital budgeting problem, if either project 1 or project 2 is selected, then project 5 cannot be selected. Which of the alternatives listed below correctly models this situation?
a) x1 + x2 + x5 1
b) x1 + x2 + x5 1
c) x1 + x5 1, x2 + x5 1
d) x1 - x5 1, x2 - x5 1
e) x1 - x5 = 0, x2 - x5 = 0
6. Find the optimal integer solution
Max Z = 5x1+6x2
Subject to : 17x1+8x2≤136
3x1+4x2≤36
x1,x1≥0 and integer
Max Z = 5x1 + 6x2
What is the optimal solution?
a) x1 = 6, x2 = 4, Z = 54
b) x1 = 3, x2 = 6, Z = 51
c) x1 = 2, x2 = 6, Z = 46
d) x1 = 4, x2 = 6, Z = 56
e) x1 = 0, x2 = 9 Z = 54