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 April 16, 2024 by Teachoo

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 = 3𝑥−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=𝑝𝑥 + 𝑞𝑦, where 𝑝,𝑞>𝑜 be the objective function. Find the condition on 𝑝 and 𝑞 so that the maximum value of 𝑍 occurs at B(4,10)𝑎𝑛𝑑 C(6,8). Also mention the number of optimal solutions in this case.

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 = 3𝑥 − 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 − 4y
Thus,
Max Z = 12 at (4, 0)
Min Z = −32 at (0, 8)
Question 38 (Choice 2) – (ii) Let 𝑍 = 𝑝𝑥 + 𝑞𝑦,where 𝑝,𝑞>𝑜 be the objective function. Find the condition on 𝑝 and 𝑞 so that the maximum value of 𝑍 occurs at B(4, 10) 𝑎𝑛𝑑 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 − 8q = 6p − 4p
2q = 2p
q = p
Also,
Number of Optimal Solutions are infinite

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.

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