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1. Given Lagrange multiplier to optimize the function z = xy subject to xty=6 a) Write the Lagrange function b) Find the optimal level of x*, y* and y*. c) Calculate the stationary value of z* 2. Given Lagrange multiplier to optimize the function z=xz+yz subject to x + 4y = 2 a) Write the Lagrange function b) Find the optimal level of x*, y* and y*. c) Calculate the stationary value of z* 3. Given Lagrange multiplier to optimize the function z = x- 3y - xy subject to xty =6 a) Write the Lagrange function b) Find the optimal level of x*, y* and y*. c) Calculate the stationary value of z*4. Determine whether the following functions are homogeneous. If so, what degree? a] x + 3y b] 4x2 + yz c) x3 +yz dj x4+ y+ +21. (a) z = xy + 1(6 - x - y) (b) x = 3, y = 3,1 = 3 (c) z =9 2. (a) z= x ty? + 1(2 - x - 4y) 8 ( b ) x = =,y= 4 17 17 (OZ = = 3. (a) z = x - 3y - xy + 1(6 - x - y) (b) x = 1, y = 5,1 = -4 (c) z = 19 4. (a) Homogeneous of degree 1 (b) Homogeneous of degree 2 (c) Not homogeneous (d) Not homogeneous