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# MCQs on LPP, IPP

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15. Find the correct constraint 3

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

16. Find the Optimal Integer Solution 1
Consider the following integer linear programming problem

(Problem in the attached word file)

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

17. Find the optimal integer solution 2

Find the optimal value of z.

a) 54 b) 55 c) 60 d) 61

18. Find the Optimal Integer Solution 3
18. Find the Optimal Integer Solution 3
Max Z=3x1+5x2
Subject to: 7x1+12x2<=136
3x1+5x2<=36
x1, x2>=0 and integer

Find the optimal value of z.

a) 30 b) 32 c) 36 d) 38

19. 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

20. Find the optimal integer solution
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