Corner points of the feasible region for a linear programming problem are (0, 2), (3, 0), (6, 0), (6, 8) and (0,5). Let F = 4x + 6y be the objective function. Then the minimum value of F occurs at :
Answer & explanation
Correct answer: option 4
Objective function F(x, y) = 4x + 6y
| Corner points | Value of F at points | |
| (0, 2) | F(0, 2) = 0 + 6 × 2 = 12 | Minimum value occurs at line joining two points on all points of line. |
| (3, 0) | F(3, 0) = 4 × 3 + 0 = 12 | |
| (6, 0) | F(6, 0) = 4 × 6 + 0 = 24 | |
| (6, 8) | F(6, 8) = 6 × 4 + 6 × 8 = 72 | |
| (0, 5) | F(0, 5) = 0 + 6 × 5 = 30 | |