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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 𝑍 = 3π‘₯βˆ’4𝑦 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 𝑍=𝑝π‘₯ + π‘žπ‘¦, where 𝑝,π‘ž>π‘œ be the objective function. Find the condition on 𝑝 and π‘ž so that the maximum value of 𝑍 occurs at B(4,10)π‘Žπ‘›π‘‘ C(6,8). Also mention the number of optimal solutions in this case.

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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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Learn in your speed, with individual attention - Teachoo Maths 1-on-1 Class


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) – (i) Let 𝑍 = 3π‘₯ βˆ’ 4𝑦 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 
= 3x βˆ’ 4y Thus, Max Z = 12 at (4, 0) Min Z = βˆ’32 at (0, 8) Question 38 (Choice 2) – (ii) Let 𝑍 = 𝑝π‘₯ + π‘žπ‘¦,where 𝑝,π‘ž>π‘œ be the objective function. Find the condition on 𝑝 and π‘ž so that the maximum value of 𝑍 occurs at B(4, 10) π‘Žπ‘›π‘‘ 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 βˆ’ 8q = 6p βˆ’ 4p 2q = 2p q = p Also, Number of Optimal Solutions are infinite

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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.