Question: What is the maximum value of the objective function C = 4x + 3y subject to the constraints x ≥ 0, y≥ 0, x + y ≤ 4?
A ) 12
B ) 16
C ) 0
D ) 18
Steps to derive
1 Objective function is C = 4x + 3y
2 Constraints are x ≥ 0, y ≥ 0, x + y ≤4.
3 The feasible region determined by the given constraints is shown in the graph.
[Draw the constraints.]
4 From the graph, the three vertices are (0, 0), (4, 0) and (0, 4).
5 To evaluate the minimum or maximum values of C, we evaluate C = 4x + 3y at each of the three vertices.
6 At (0, 0) , C = 4(0) + 3(0) = 0
[Substitute the values.]
7 At (4, 0) , C = 4(4) + 3(0) = 16
[Substitute the values.]
8 At (0, 4) , C = 4(0) + 3(4) = 12
[Substitute the values.]
9 So, the maximum value of the objective function, C is 16.
Hence the right answer is Option C
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