On a production line, purchase of a new machine will increase production rate but because of high purchasing price annual profit will decrease. These two attributes (production rate (x1) and annual profit (x2)) are mutually utility independent. The range for x1 (in 1,000 units) is [20,50] and range for x2 (in $100,000) is [1,5]. The individual utility functions are given as: (x1-20) U1(x1)= = 900 and (x2 - 1) U2(x2)= = 16 Suppose that decision maker is indifferent between Alternative 1 and Alternative 2 Alternative 1: (x1-32, x2=3) Alternative 2: A lottery between (x1-50, x2=5) and (x1-20, x2-1) with probabilities 0.4 and 0.6, respectively and also between Alternative 3 and Alternative 4 Alternative 3: (x1-50, x2=1) Alternative 4: A lottery between (x1-50, x2=5) and (x1-20, x2-1) with probabilities 0.6 and 0.4, respectively For the multilinear utility function, i.e., U(x1, x2)=k1 U1(x1)+k2*U2(x2)+(1-k1-k2)*U1(x1)*U2(x2) k1 is 0.44 k2 s 0.36 x1 and x2 are 1.37 Now, assume that k1=0.6, k2=0.8 and we have Machine 1 and Machine 2 with following information. Probability Outcome (x1,x2) Machine 1 0.7 0.3 (35,4) (25,3) EU (Machine 1 Substitutes Machine 2 Probability Outcome (x1,x2) 0.4 (45,3) 0.6 (30, 2)