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Question
The point which provides the solution to the linear programming problem: Max P = 2x + 3y subject to constraints: x ≥ 0, y ≥ 0, 2x + 2y ≤ 9, 2x + y ≤ 7, x + 2y ≤ 8, is ______
Options
(3, 2.5)
(2, 3.5)
(2, 2.5)
(1, 3.5)
MCQ
Fill in the Blanks
Solution
The point which provides the solution to the linear programming problem: Max P = 2x + 3y subject to constraints: x ≥ 0, y ≥ 0, 2x + 2y ≤ 9, 2x + y ≤ 7, x + 2y ≤ 8, is (1, 3.5).
Explanation:
Feasible region lies on the origin side of all lines and in the first quadrant.
The comer points of the feasible region are
O(0, 0), A(0, 4), B`(1, 7/2)`, C`(5/2, 2)`, D`(7/2, 0)`
Substituting the above points in P = 2x + 3y, we get
Max P = 12.5 at B `(1, 7/2)`
∴ B ≡ (1, 3.5)
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