CBSE Class 12 Sample Paper for 2021 Boards

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Question 38 (Choice 2) - CBSE Class 12 Sample Paper for 2021 Boards - Solutions of Sample Papers and Past Year Papers - for Class 12 Boards

Last updated at August 10, 2026 by

The corner points of the feasible region determined by the system of linear constraints are as shown below:
Answer each of the following:

(i) Let š‘ = 3š‘„−4š‘¦ be the objective function. Find the maximum and minimum value of Z and also the corresponding points at which the maximum and minimum value occurs.

(ii) Let š‘=š‘š‘„ + š‘žš‘¦, where š‘,š‘ž>š‘œ be the objective function. Find the condition on š‘ and š‘ž so that the maximum value of š‘ occurs at B(4,10)š‘Žš‘›š‘‘ C(6,8). Also mention the number of optimal solutions in this case.

 

The corner points of feasible region determined by system of linear

Question 38 (Choice 2) - CBSE Class 12 Sample Paper for 2021 Boards - Part 2

Question 38 (Choice 2) - CBSE Class 12 Sample Paper for 2021 Boards - Part 3

 

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Transcript

Question 38 (Choice 2) The corner points of the feasible region determined by the system of linear constraints are as shown below: Question 38 (Choice 2) ā€“ (i) Let š‘ = 3š‘„ āˆ’ 4š‘¦ be the objective function. Find the maximum and minimum value of Z and also the corresponding points at which the maximum and minimum value occurs. Checking value of Z at corner points Corner Points Value of Z ā€Ø= 3x āˆ’ 4y Thus, Max Z = 12 at (4, 0) Min Z = āˆ’32 at (0, 8) Question 38 (Choice 2) ā€“ (ii) Let š‘ = š‘š‘„ + š‘žš‘¦,where š‘,š‘ž>š‘œ be the objective function. Find the condition on š‘ and š‘ž so that the maximum value of š‘ occurs at B(4, 10) š‘Žš‘›š‘‘ C(6, 8). Also mention the number of optimal solutions in this case. Since Maximum Z occurs at B (4, 10) and C (6, 8) Thus, 4p + 10q = 6p + 8q 10q āˆ’ 8q = 6p āˆ’ 4p 2q = 2p q = p Also, Number of Optimal Solutions are infinite

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