# Linear programming MCQs

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1. A furniture maker produces tables and chairs. Each product must go through a three stage manufacturing process assembly, finishing, and inspection. Each table requires 3 hours of assembly, 2 hours of finishing, and 1 hour of inspection. Each chair requires 2 hours of assembly, 2 hours or finishing, and 1 hour of inspection. The profit per table is $120; the profit per chair is $80. Each week there are 200 hours of assembly time available, 180 hours of finishing time, and 40 hours of inspection time. Linear programming is to be used to develop a production schedule. Define the variables as follows:

T = number of tables produced each week

C = number of chairs produced each week

According to the above Exhibit, which describes a production problem, which of the following would be necessary constraint in the problem?

a. T + C < 40

b. T + C < 200

c. T + C < 180

d. 120T + 80C > 1000

2. A furniture maker produces tables and chairs. Each product must go through a three stage manufacturing process assembly, finishing, and inspection. Each table requires 3 hours of assembly, 2 hours of finishing, and 1 hour of inspection. Each chair requires 2 hours of assembly, 2 hours or finishing, and 1 hour of inspection. The profit per table is $120; the profit per chair is $80. Each week there are 200 hours of assembly time available, 180 hours of finishing time, and 40 hours of inspection time. Linear programming is to be used to develop a production schedule. Define the variables as follows:

T = number of tables produced each week

C = number of chairs produced each week

According to the above Exhibit, which describes a production problem, what is the objective function?

a. Maximize T + C

b. Maximize 120T + 80C

c. Maximize 200T + 200 C

d. Minimize 6T + 5C

3. Considering the following linear programming problem:

Maximize 40 X + 30 X2 + 60X2

Subject to: X1 + X2 + X3 > 90

12X1 + 8X2 + 10X3 < 1500

X1, X2, X3>0

How many slack, surplus, and artificial variables would be necessary if the simplex were used to solve the problem?

a. 3 slack, 3 surplus, and 3 artificial

b. 1 slack, 2 surplus, and 2 artificial

c. 1 slack, 4 surplus, and 4 artificial

d. 1 slack, 1 surplus, and 1 artificial

4. A feasible solution to a linear programming problem

a. Must satisfy all of the problem's constraints simultaneously

b. Need not satisfy all of the constraints, only the non-negativity constraints

c. Must be a corner point of the feasible region

d. Must give the maximum possible profit

5. Production scheduling is amenable to solution by linear programming because

a. The optimal product combination will minimize production risk

b. Linear programming will allow investment losses to be minimized

c. Scheduling requires specific, narrowly defined constraints

d. Objective functions and constraints can be readily developed and are relatively stable over time

6. The Cj - Zj of a simplex tableau gives

a. The number of units of each basic variable that must be removed from the solution if a new variable is entered

b. The gross profit loss given up by adding one unit of a variable into the solution

c. The next profit or loss that will result from introducing one unit of the variable indicated in that column into the solution

d. The maximal value a variable can take on and still have all constraints satisfied

7. Which of the following is NOT a part of every linear programming problem formulation?

a. An objective function

b. A set of constraints

c. Non-negativity constraints

d. A redundant constraint

8. The number -2 in the X2 column and X1 row of a simplex tableau implies that

a. If 1 unit of X2 is added to the solution, X1 will decrease by 2

b. If 1 unit of X1 is added to the solution, X2 will decrease by 2

c. If 1 unit of X2 is added to the solution, X1 will increase by 2

d. If 1 unit of X1 is added to the solution, X2 will increase by 2

9. What is the maximum possible value for the objective function in the linear programming problem?

Maximize 12X + 10Y

Subject to: 4X + 3Y < 480

2X + 3Y < 360

all variables >0

a. 360

b. 480

c. 1520

d. 1560

10. Which of the following is NOT true about slack variables in a simplex tableau?

a. They are used to convert ,,T constraint inequalities to equations

b. They represent unused resources

c. They require the addition of an artificial variable

d. They yield no profit

11. Using linear programming to maximize audience exposure in an advertising campaign is an example of the type of linear programming application known as:

a. Media selection

b. Marketing research

c. Portfolio assessment

d. Media budgeting

12. The substitution rate give

a. The Number of units of each basic variable that must be removed from the solution if a new variable is entered

b. The gross profit or loss given up by adding one unit of a variable into the solution

c. The net profit or loss that will result from introducing one unit of the variable indicted in that column into the solution

d. The maximal value a variable can take on and still have all the constraints satisfied

13. Which of the following is NOT a property of all linear programming problems?

a. The presence of restrictions

b. Optimization of some objective

c. The need for a computer program

d. Alternate courses of action to choose from

14. The following does not represent a factor a manager might consider when employing linear programming from a production scheduling:

a. Labor capacity

b. Space limitations

c. Product demand

d. Risk assessment

15. The graphical solution to a linear programming problem

a. Includes the corner point method and the isoprofit line solution method

b. Is useful for four or fewer decision variables

c. Is inappropriate for more than two constraints

d. Is the most difficult approach, but is useful as a learning tool

16. The selection of specific investments from among a wide variety of alternatives is the type of LP problem known as

a. The product mix problem

b. The investment banker problem

c. The Wall Street problem

d. The portfolio selection problem

17. Consider the following general form of a linear programming problem:

Maximize Profit

Subject to: Amount of resource A used < 100 units

Amount of resource B used < 240 units

Amount of resource B used < 150 units

The shadow price for S1 is 25, for S2 is 0, and for S3 is 40. If the right-hand side of the constraint 1 is changed from 100 to 101, what happens to maximum possible profit?

a. It would increase by 25

b. It would decrease by 25

c. It would increase by 40

d. It would decrease by 40

18. Determining the most efficient allocation of people, machines, equipment, etc., is characteristic of the LP problem type know as

a. Production scheduling

b. Labor planning

c. Assignment

d. Blending

19. The corner point solution method

a. Will yield different results from the isoprofit line solution method

b. Requires that the profit all corners of the feasible region be compared

c. Will provide one, and only one, optimum

d. Requires that all corners created by all constraints be compared

20. In a maximization problem, when one or more of the solution variables and the profit can be made infinitely large without violating any constraints, then the linear program has

a. An infeasible solution

b. An unbounded solution

c. A redundant constraint

d. Alternate optimal solutions

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