# NCERT Class 12-Mathematics: Chapter – 12 Linear Programming Part 9 (For CBSE, ICSE, IAS, NET, NRA 2022)

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## Fill in the Blanks in Each of the Exercises 35 to 41

**Question 35**:

In a LPP, the linear inequalities or restrictions on the variables are called ________.

**Answer**:

Linear constraints

**Question 36**:

In a LPP, the objective function is always ________

**Answer**:

Linear

**Question 37**:

If the feasible region for a LPP is ________, then the optimal value of the objective function may or may not exist.

**Answer**:

Unbounded

**Question 38**:

In a LPP if the objective function has the same maximum value on two corner points of the feasible region, then every point on the line segment joining these two points give the same ________ value.

**Answer**:

Maximum

**Question 39**:

A feasible region of a system of linear inequalities is said to be ________ if it can be enclosed within a circle.

**Answer**:

Bounded

**Question 40**:

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

**Answer**:

Intersection

**Question 41**:

The feasible region for an LPP is always a ________ polygon.

**Answer**:

Convex

### State Whether the Statements in Exercises 42 to 45 Are True or False

**Question 42**:

If the feasible region for a LPP is unbounded, maximum or minimum of the objective function may or may not exist.

**Answer: True**

**Question 43**:

Maximum value of the objective function in a LPP always occurs at only one corner point of the feasible region.

**Answer: False**

**Question 44**:

In a LPP, the minimum value of the objective function is always if origin is one of the corner point of the feasible region.

**Answer: False**

**Question 45**:

In a LPP, the maximum value of the objective function is always finite.

**Answer: True**