Finite Mathsection 3.3 Linear Programming: A geometric approachTerms: Constraints, Objective functions, Feasibile regionEx1, Let z = 2x + y subject to Find max z and min z.x + y 5xy 1x 0, y 01 2 3 4 5 67-1-2-3-4-5-6-712345-1-2-3-4-5 Ex2, Let z = 50x + 40y subject to Find max z and min z.x + 2y 102x + y 8 x 0, y 0ŸŸ1 2 3 4 5 67-1-2-3-4-5-6-712345-1-2-3-4-5 Ex3, Let z = 30x + 60y subject to Find max z and min z.x + 2y 102x + y 8 x 0, y 0ŸŸEx4, Let z = 30x + 70y subject to Find min z.x + 2y 52x + y 4 y 01 2 3 4 5 67-1-2-3-4-5-6-712345-1-2-3-4-5 Ex5, Let z = 60x + 70y subject to Find max z and min z.x + 2y 52x + y 4 y 0Ex6, Let z = 30x + 50y subject to Find max z and min z.y x + 2y 3x 2x0Ÿ Ÿ1 2 3 4 5 67-1-2-3-4-5-6-712345-1-2-3-4-5 Ex7, Let z = 30x 50y subject to Find max z and min z.y x + 2y 3x 2x0Ÿ ŸEx8, Find the maximum of z = 45x + 75y subject to y 2x + 44x +2y 1šŸ1 2 3 4 5 67-1-2-3-4-5-6-712345-1-2-3-4-5 Ex9, + 2y 6+ x 0, y 0x3y2Ÿ2x 7 (a) Find the maximum of z = 40x + 50y (b) Find the maximum of z = 20x + 200y (c) Find the minimum of z = 30x
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