# NCERT Class 12-Mathematics: Chapter – 12 Linear Programming Part 3 (For CBSE, ICSE, IAS, NET, NRA 2023)

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## Long Answer (L. A.)

**Question 5**:

Refer to Example 4. Solve the LPP.

**Answer**:

The problem is:

Maximise

subject to the constraints:

The feasible region OABC is shown in the Fig. 12.4.

Since the feasible region is bounded, therefore maximum of Z must occur at the corner point of OBC.

Corner Point | Value of Z |

Thus, maximum Z is at the point , i.e.. , the company should produce black and white television sets and coloured television sets to get maximum profit.

**Question 6**:

Minimise subject to the constraints:

**Answer**:

We first draw the graphs of . The shaded region ABCD is the feasible region (R) determined by the above constraints. The feasible region is unbounded. Therefore, minimum of Z may or may not occur. If it occurs, it will be on the corner point.

Corner Point | Value of Z |

Let us draw the graph of as shown in Fig. 12.5 by dotted line.

We see that the open half plane determined by and R do not have a point in common. Thus, is the minimum value of .

## Objective Type Questions

Choose the correct answer from the given four options in each of the Examples 7 to 8.

**Question 7**:

The corner points of the feasible region determined by the system of linear constraints are . Let , where . Condition on and so that the maximum of Z occurs at both the points and is

(A)

(B)

(C)

(D)

**Answer**:

The correct answer is (D) . Since Z occurs maximum at and , therefore, .

**Question 8**:

Feasible region (shaded) for a LPP is shown in the Fig. 14.6. Minimum of occurs at the point

(A)

(B)

(C)

(D)

**Answer**:

The correct answer is (B) .