Minimize z=-3x+4u subject to the constraints
`x+2y le 8`
`3x+2y le 12`
` x ge 0, y ge 0` by graphical method.

(a)Maximise z = 4x + y subject to constraints : x + y le 50 3x + y le 90 x ge 0 y ge 0 by graphical method. (b) Find the value of K, if f(x) = {{:(Kx + 1, "if"x le pi),(cos x, "if " x gt pi):} is continuous at x = pi .

a. Minimize z =-3x+4y subject to constraints. x+2yle8 3x+2yle12 xge0, yge0 by graphical method. b. Prove that {:abs((1,a,a^2),(1,b,b^2),(1,c ,c^2)):} = (a - b)(b-c)(c-a)

Minimize and Maximize z=600x+400y Subject to the constraints : x+2y le 12 2x+y le 12 4x+5y ge 21 and xge0,y ge 0 graphical method.

Maximize Z = 3x + 5y, subject to constraints are x + 3y le 3, x + y le 2 " and " x ,y ge 0 .

Minimize and Maximize Z = 3x + 9y subject to the constraints x+3ylt=60 x+y gt=10 xlt=y x gt= 0 , y gt= 0 by the graphical method .

Maximize Z = 3x + 4y , subject to the constraints are x + y le 4, x ge 0 " and " y ge 0 .

Maximize Z = 3x + 2y, subject to constraints are x + 2y le 10, 3x + y le 15, " and " x , y ge 0 .