Janet has to select among three different machines: A, B, and C. She is concerned about the resulting reliability (r) and purchase cost (c). She developed a constructed scale and evaluated the three alternatives with scores between 0 (the least desired) and 10 (the most desired). In terms of (r, c) scores, Machine A is will produce an outcome of (6,8), whereas Machine B will do (4,6). Machine C, on the other hand, is unreliable: It will produce an outcome of (5,9) with probability p, and (8,7) with probability 1p. a- For what range of p values there is no conflict among the attributes with regard to the optimal choice? That is, for which p values a particular alternative is the best in both attributes? Do not forget to indicate which machine is the optimal for a p range you identify. For the rest of the question, use p=0.7. Assume that the mutual utility independence assumption holds for Janet and she is risk-neutral with respect to both attributes. Also, - She is indifferent between a sure outcome of (5,2) vs. [an uncertain outcome with probability 2/3 of (6,0) and probability 1/3 of (0,9)]. - She is indifferent between a sure outcome of (4,8) vs. [an uncertain outcome with probability 0.5 of (10,0) and probability 0.5 of (0,10)]. b- Determine the exact multi-attribute utility function U(r,c) for Janet. c- Does Janet consider reliability and purchase cost as substitutes, complements or neither? d- Based on the utility function you found, which machine should Janet select