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 ๐‘ = 3๐‘ฅ−4๐‘ฆ 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 ๐‘=๐‘๐‘ฅ + ๐‘ž๐‘ฆ, where ๐‘,๐‘ž>๐‘œ be the objective function. Find the condition on ๐‘ and ๐‘ž so that the maximum value of ๐‘ occurs at B(4,10)๐‘Ž๐‘›๐‘‘ 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

 

  1. Class 12
  2. Solutions of Sample Papers and Past Year Papers - for Class 12 Boards

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) โ€“ (i) Let ๐‘ = 3๐‘ฅ โˆ’ 4๐‘ฆ 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 โ€จ= 3x โˆ’ 4y Thus, Max Z = 12 at (4, 0) Min Z = โˆ’32 at (0, 8) Question 38 (Choice 2) โ€“ (ii) Let ๐‘ = ๐‘๐‘ฅ + ๐‘ž๐‘ฆ,where ๐‘,๐‘ž>๐‘œ be the objective function. Find the condition on ๐‘ and ๐‘ž so that the maximum value of ๐‘ occurs at B(4, 10) ๐‘Ž๐‘›๐‘‘ 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 โˆ’ 8q = 6p โˆ’ 4p 2q = 2p q = p Also, Number of Optimal Solutions are infinite

Class 12
Solutions of Sample Papers and Past Year Papers - for Class 12 Boards

About the Author

Davneet Singh's photo - Teacher, Engineer, Marketer
Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 10 years. He provides courses for Maths and Science at Teachoo.