# 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.

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:

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 Fig. 12.5-The Shaded Region ABCD is the Feasible Region

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)

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 Fig. 14.6-Feasible Region (Shaded) for a LPP is Shown in the …

(A)

(B)

(C)

(D)