Read the scenario below and give a detail response to the questions that follow Bill, Buster and Bryan share a dormitory room on the university campus. The dormitory offers soft drink and chips for sale in vending machines. They consistently choose between soft drink and soda to maximize their satisfaction given their utility function, income and the prices of soda and chips. The table below shows the utility function and income of the dorm mates Customer Utility Function Income Bill U(S,C)= $03CO.7 $6000 Buster U(S,C)=min(S,30) $7000 Bryan U(S,C)=25+C $4000 A. Given S is the number of soft drinks per week and C the number of bags of chips per week i. Derive the demand functions for soft drink and chips for BILL. (use both substitution method and Lagrangian method) ii. Derive the demand functions for soft drink and chips for BUSTER. 111. Explain the demand functions for soft drink and chips for BRYAN