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Q1. Problems which seek to maximise or, minimise profit or, cost form a general class of problems called ………

• Optimisation problems
• Simple problems
• Difficult problems
• Non-linear problems

Solution

A problem which seeks to maximise or minimise a linear function (say of two variables x and y) subject to certain constraints as determined by a set of linear inequalities is called an optimisation problem

Q2. Let Z = ax + by is a linear objective function. Variables x and y are called ……… variables.

• Decision
• Dependent
• Independent
• Continuous

Solution

Let Z = ax + by is a linear objective function. Variables x and y are called decision variables.

Q3. A bounded Region has?

• A bounded region will have only a maximum value.
• A bounded region will have only a minimum value.
• A bounded region will have both  maximum and minimum values.
• A bounded region will have neither a maximum or minimum value.

Solution

A bounded region will have both  maximum and minimum values.

Q4. The solution set of the inequation 2x + y > 5 is

• half plane that contains the origin
• open half plane not containing the origin
• whole xy-plane except the points lying on the line 2x + y = 5.
• points on line

Solution

Consider the following figure: Thus the solution set is the open half plane not containing the origin.

Q5. The linear inequalities on the variables of a linear programming problem are called ………

• Constraints
• Variables
• Solutions
• Non-variable values

Solution

The linear inequalities on the variables of a linear programming problem are called constraints.

Q6. Infeasibility means that the number of solutions to the linear programming models that satisfies all constraints is

• At least 1
• Zero
• An infinite number
• At least 2

Solution

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

Q7. A Corner Point is?

• A vertex of the feasible region.
• every intersection of lines.
• is the optimal solution to a linear programming problem
• all points on x axis

Solution

A vertex of the feasible region.

Q8. In a Linear programming problem Variables x and y are called ________variables.

• decision variables.
• linear variables.
• optimization variables
• Interdependent variables

Solution

decision variables

Q9. If the system of constraints has no point which satisfies all the constraints and non-negativity restrictions then the solution of a LPP is an

• Infeasible solution
• Feasible solution
• Optimal solution
• None of these

Solution

If the system of constraints has no point which satisfies all the constraints and non-negativity restrictions then the solution of a LPP is an  Infeasible solution.

Q10. A ……… of a feasible region is a point in the region, which is the intersection of two boundary lines.

• Reasonable point
• Vertex point
• Corner point
• Section point

Solution

A corner point of a feasible region is a point in the region, which is the intersection of two boundary lines.

Q11. The common region determined by all the constraints including non-negative constraints x, y ≥ 0 of a linear programming problem is called the ……...

• Feasible region
• Infeasible region
• Simple region
• Bounded region

Solution

The common region determined by all the constraints including non-negative constraints x, y ≥ 0 of a linear programming problem is called the feasible region.

Q12. Objective function of a LPP is

• A constraint
• function to be optimized
• Relation between variables
• Equation in a line

Solution

Objective function of a LPP is a function to be optimized.

Q13. All linear programming problems have all of the following properties EXCEPT

• A linear objective function that is to be maximized or minimized
• A set of linear constraints
• Alternative optimal solutions
• Variables that are all restricted to nonnegative values

Solution

Optimal solution if it exists is unique

Q14. The optimum value of the objective function is attained at the points

• On x-axis
• On y-axis
• Corner points of feasible region
• Any point of the feasible region

Solution

Corner points of feasible region

Q15. A feasible solution of a LPP if it also optimizes the objective function is called

• Optimal feasible solution
• Optimal solution
• Feasible solution
• None of these

Solution

Optimal feasible solution.

Q16. Z = ax + by, where a, b are constants, which has to be maximized or minimized is called a _________.

• Optimisation function
• Linear function
• Objective function
• Nonlinear function

Solution

Linear function Z = ax + by, where a, b are constants, which has to be maximized or minimized is called a linear objective function.

Q17. Problems where we have to minimise a linear function subject to certain conditions determined by a set of linear inequalities with variables as non-negative are called …......

• Simple Problems
• Non-Linear Programming Problems
• Linear Programming Problems
• Difficult Problems

Solution

Problems where we have to minimise a linear function subject to certain conditions determined by a set of linear inequalities with variables as non-negative. Such problems are called Linear Programming Problems.

Q18. The set of all feasible solutions of a LPP is a ____ set.

• Concave
• Convex
• Feasible
• None of these

Solution

The set of all feasible solutions of a LPP is a CONVEX set.

Q19. Which of the following statements is not true

• The solution region of the system of linear inequalities, is called Infeasible region
• The set of all feasible solutions of a LPP is a convex set
• A set of values of variables is called a solution of a LPP, if it satisfies the constraints of the LPP
• A set is a convex set ,if every point on the line segment joining any two points in it lies in it

Solution

The solution region of the system of linear inequalities  ,is called feasible region.

Q20. Let Z = ax + by be the objective function at each corner point. Let m and n, respectively denote the largest and smallest values of these points. When the feasible region is ………, m and n are the maximum and minimum values of Z.

• Unshaded
• Shaded
• Unbounded
• Bounded