1. Find the Hessian matrices of and determine whether there are convex or concave: (a) f(1,2)=4x-3x...

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1. Find the Hessian matrices of and determine whether there are convex or concave: (a) f(1,2)=4x-3x (b) f(x1,x2)=2x-6x122 (c) f(x1,2)= ln(2x1 - 3x2) (d) f(21, 22)=2x+2x 2. Solve the following problems: maxima or minima. (a) (b) max [Inx1+2lnz2] s.t. 3x1 +5x2 = 180 (1) 1.2 max [221 +4x2] s.t. 1+2x2 = 180 (2) (c) #1.22 max [30-- s.t. 1+2=100 #1,2 (3) (d) min [(1-3)2 + (2-5)2] s.t. 21 + x2 = 100 (4) 21.22 1. Find the Hessian matrices of and determine whether there are convex or concave: (a) f(1,2)=4x-3x (b) f(x1,x2)=2x-6x122 (c) f(x1,2)= ln(2x1 - 3x2) (d) f(21, 22)=2x+2x 2. Solve the following problems: maxima or minima. (a) (b) max [Inx1+2lnz2] s.t. 3x1 +5x2 = 180 (1) 1.2 max [221 +4x2] s.t. 1+2x2 = 180 (2) (c) #1.22 max [30-- s.t. 1+2=100 #1,2 (3) (d) min [(1-3)2 + (2-5)2] s.t. 21 + x2 = 100 (4) 21.22