Maximize :
`z=3x+5y`
Subject to : `x+4y le 24`
`3x+y le 21`
`x+y le 9`
`x ge 0, y ge 0`

x + y le 10, 4x + 3y le 24,x ge 0, y ge 0

Maximize z = 6 x + 4y , subject to 2x + 3y le 30, 3x + 2y le 24, x + y ge 3, x ge 0 , y ge0.

Maximize z = 4 x + 5y , subject to 2x + y ge7, 2x + 3 y le 15, x le 3, x ge 0 , y ge 0

Solve the following linear programming problem graphically : Maximize : z = 4x + y Subject to the constraints : x + y le 50 3x + y le 90 x ge 0, y ge 0

Z = 4x + y x + y le 50, 3x + y le 90, x ge 0, y ge 0

Optimum solution of the L.P.P. : Maximize z= 3x+5y subject to 3x+2y le 18, x le 4, y le 6, x ge 0, y ge 0 is

Maximise Z=x+y subject to x+4y le 8 , 2x+3y le 12, 3x+y le 9, x ge 0, and y ge 0

Maximize X = 8x + 9y Subject to 2x + 3y le 6 3x - 2y le 6 y le 1 x, y ge 0

Maximise z = x + y subject ot x+4y le 8, 2x+3y le 12, 3x+y le 9, x ge 0, y ge 0 .