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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

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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) – (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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