(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)

(a) Minimize and Maximize z=600x+400y Subject to the constraints : x+2yle12 2x+yle12 4x+5yge20 and xge0, y ge0 by graphical method. (b) Find the value of k, if f(x)={{:((kcosx)/(pi-2x)",",xne(pi)/(2)),(3",",x=(pi)/(2)):} is continuous at x=(pi)/(2) .

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.

(a) Minimise and Maximise z=5x+10y subject to constraints : x+2y le 120 , x+y ge60 , x-2y ge 0 , x gt 0 and y ge 0 by graphical method. (b) Find the value of K if f(x)={(Kx+1," if "x le 5),(3x-5," if "x gt5):} is continuous at x = 5.

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 .

(a) Minimze and maximize Z=5x+10y subject to the constraints x+2yle120 x+ge60 x-2yge0andxge0,yge0 , by graphical method. (b) Find the value of k, if {:(f(x)=(1-cos2x)/(1-cosx),xne0),(=k,x=0):} is continuous at x=0 .