The maximum value of Z=3 x+4 y for the given constraints x+2 y 76,2 x+y 104, x 0, y 0 is

Step-by-step solution

The constraints are x + 2y 76 , 2x + y 104 , x 0 , and y 0 . The corner points of the feasible region are found by solving the intersection of the boundary lines and the axes. 1. Intersection of x + 2y = 76 and 2x + y = 104 : Multiply the first equation by 2: 2x + 4y = 152 . Subtract the second equation: (2x + 4y) - (2x + y) = 152 - 104 3y = 48 y = 16 . Substitute y = 16 into x + 2(16) = 76 x + 32 = 76 x = 44 . Corner point: (44, 16) . 2. Intersection of x + 2y = 76 with the y-axis ( x=0 ): 2y = 76 y = 38 . Corner