NCERT Class 12-Mathematics: Chapter –12 Linear Programming Part 3
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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).