Question

Determine the minimum value of the objective function, C.

C = 3x + 2y

x+y≥4
x>0
y>0

Enter your answer

C=

Answer 1

c = 8

Explanation:

The points (x,y) satisfying the constraint x + y ≥ 4 the set of all the points to the right of the line x + y = 4. Now since, minimum or maximum occurs only on the edges we consider the points (0,4) and (4,0).

These would also represent the minimum points as this system is unbounded.

The given subjective function is: c = 3x + 2y

Substituting (0,4) and (4,0) we get:

At (4,0) = 3(4) + 2(0) = 12

At (0,4) = 3(0) + 2(4) = 8

Clearly, at (0,4) we have the minimum value and the minimum value is 8.