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

Last updated at Oct. 27, 2020 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 ๐ = 3๐ฅ−4๐ฆ 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=๐๐ฅ + ๐๐ฆ, where ๐,๐>๐ be the objective function. Find the condition on ๐ and ๐ so that the maximum value of ๐ occurs at B(4,10)๐๐๐ C(6,8). Also mention the number of optimal solutions in this case.

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 = 3๐ฅ โ 4๐ฆ 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 โจ= 3x โ 4y
Thus,
Max Z = 12 at (4, 0)
Min Z = โ32 at (0, 8)
Question 38 (Choice 2) โ (ii) Let ๐ = ๐๐ฅ + ๐๐ฆ,where ๐,๐>๐ be the objective function. Find the condition on ๐ and ๐ so that the maximum value of ๐ occurs at B(4, 10) ๐๐๐ 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 โ 8q = 6p โ 4p
2q = 2p
q = p
Also,
Number of Optimal Solutions are infinite

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 9 years. He provides courses for Maths and Science at Teachoo.