Find the minimum value of c=2x+y subject to the following constraints:
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The minimum value of C is 20

Step-by-step 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