Answer:
The minimum value of C is 20
Explanation:
Sketch the constraints, that is sketch
2x + 3y = 24
with intercepts (0, 8 ) and (12, 0 )
4x + y = 38
with intercepts (0, 38 ) and (9.5, 0 )
The solutions lie above both lines
Solve 2x + 3y = 24 and 4x + y = 38 simultaneously to find point of intersection at (9, 2 )
The vertices of the feasible region are at
(0, 38), (9, 2) and (12, 0)
Evaluate the objective function for each of these vertices
C = 2(0) + 38 = 0 + 38 = 38
C = 2(9) + 2 = 18 + 2 = 20
C = 2(12) + 0 = 24 + 0 = 24
The minimum value of C is 20 when x = 9 and y = 2