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Question: Find the maximum value of the function C = 7x + y subject to the constraints x ≥ 0, y ≥ 0 , 5x + 3y ≤ 15.


A ) 22
B ) 5
C ) 21
D ) 9

Steps to derive

1 Objective function is C = 7x + y

2 Constraints are x ≥ 0, y ≥ 0, 5x + 3y ≤ 15

3 The feasible region determined by the given constraints is shown.
 [Draw the graph.]


4 From the graph, the three vertices are (0, 0), (3, 0) and (0, 5).

5 To evaluate the minimum, maximum values of C , we evaluate C = 7x + y at each of the vertices.

6 At (0, 0) , C = 7(0) + (0) = 0
 [Substitute the values.]

7 At (3, 0) , C = 7(3) + (0) = 21
 [Substitute the values.]

8 At (0, 5) , C = 7(0) + (5) = 5
 [Substitute the values.]

9 So, the maximum value of C is 21.



Hence the right answer is Option C

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