# MCQs on LPP

1. Decision variables

a. tell how much or how many of something to produce, invest, purchase, hire, etc.

b. represent the values of the constraints.

c. measure the objective function.

d. must exist for each constraint.

2. Which of the following is a valid objective function for a linear programming problem?

a. Max 5xy

b. Min 4x + 3y + (2/3)z

c. Max 5x2 + 6y2

d. Min (x1 + x2)/x3

3. Which of the following statements is NOT true?

a. A feasible solution satisfies all constraints.

b. An optimal solution satisfies all constraints.

c. An infeasible solution violates all constraints.

d. A feasible solution point does not have to lie on the boundary of the feasible region.

4. To find the optimal solution to a linear programming problem using the graphical method

a. find the feasible point that is the farthest away from the origin.

b. find the feasible point that is at the highest location.

c. find the feasible point that is closest to the origin.

d. None of the alternatives is correct.

5. The improvement in the value of the objective function per unit increase in a right-hand side is the

a. sensitivity value.

b. dual price.

c. constraint coefficient.

d. slack value.

6. Infeasibility means that the number of solutions to the linear programming models that satisfies all constraints is

a. at least 1.

b. 0.

c. an infinite number.

d. at least 2.

7. A constraint that does not affect the feasible region is a

a. non-negativity constraint.

b. redundant constraint.

c. standard constraint.

d. slack constraint.

8. All linear programming problems have all of the following properties EXCEPT

a. a linear objective function that is to be maximized or minimized.

b. a set of linear constraints.

c. alternative optimal solutions.

d. variables that are all restricted to nonnegative values.

PART B ¡V PROBLEMS (30 POINTS EACH)

1. Consider the following linear programming problem

Max 8X + 7Y

s.t. 15X + 5Y < 75

10X + 6Y < 60

X + Y < 8

X, Y ?d 0

a. Set up and solve using Lindo.

b. What are the values of X and Y at the optimal solution?

c. What is the optimal value of the objective function?

5. Use this graph to answer the questions.

Max 20X + 10Y

s.t. 12X + 15Y < 180

15X + 10Y < 150

3X - 8Y < 0

X , Y > 0

a. Which area (I, II, III, IV, or V) forms the feasible region?

b. Which point (A, B, C, D, or E) is optimal?

c. Which constraints are binding?

d. Which slack variables are zero?

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#### Solution Summary

This posting contains solution to following MCQs on Linear programming problems.

MCQs on LPP, IPP

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

Answer: ___________

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

Answer: _____

17. Find the optimal integer solution 2

Find the optimal value of z.

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

Answer: _____

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

Answer: _____

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

Answer: _____

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