# NCERT Class 12-Mathematics: Chapter –12 Linear Programming Part 9

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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**