A decision analyst is asked to asses a multi attribute utility function for the government that wishes to revise its healthcare policies. The team identified the cost and the quality of care provided to be the two main attributes in this context. They agreed to assume that these attributes satisfy utility independence. By using reference lotteries, they obtained the following information on utility functions uC (c) for cost and uQ(q) for quality of care:

(i) The government is indifferent between the certain outcome (c, q) with uC (c) = 0.7 and uQ(q) = 0.2, and getting best cost-worst quality with probability 0.65 and worst cost-best quality with probability 0.35.

(ii) The government is also indifferent between the certain outcome of best cost-worst quality, and getting best cost-best quality with probability 0.6 and worst cost-worst quality with probability 0.4.

Suggest a utility function for this government and justify your suggestion. Are cost and quality substitutes or complements with respect to the utility function you suggested? Why?