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Question: What are the minimum and maximum values of the objective function P = 5x + 6y subject to the constraints x ≥ 2, x ≤ 4, y ≥ 1, y ≤ 3?


A ) 28, 38
B ) 26, 28
C ) 16, 38
D ) 16, 28

Steps to derive

1 Objective function is P = 5x + 6y

2 Constraints are x ≥ 2, x ≤ 4, y ≥ 1, y ≤ 3

3 The feasible region determined by the above constraints is shown.


4 From the figure the vertices are (2, 1), (4, 1), (2, 3) and (4, 3).

5 At (2, 1), P = 5(2) + 6(1) = 16
 [Substitute the values.]

6 At (4, 1), P = 5(4) + 6(1) = 26
 [Substitute the values.]

7 At (2, 3), P = 5(2) + 6(3) = 28
 [Substitute the values.]

8 At (4, 3), P = 5(4) + 6(3) = 38
 [Substitute the values.]

9 So, the minimum and maximum values of P are 16 and 38.



Hence the right answer is Option C

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