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 dormi soft drink and chips for sale in vending machines. They consistently choose between and soda to maximize their satisfaction given their utility function, income and the prid 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,3C) $7000 Bryan U(S,C)=28+C $4000 A. Given S is the number of soft drinks per week and C the number of bags of chips p i. Derive the demand functions for soft drink and chips for BILL. substitution method and Lagrangian method) ii. Derive the demand functions for soft drink and chips for BUSTER. iii. Explain the demand functions for soft drink and chips for BRYAN. B. If soft drink is priced at $100 each, chips $50 per bag per week to spend on chip drink, i. Complete the table showing the optimal amount of soft drink (S*) and chip utility value (U*) for each person? Bill Buster Bryan ii. Suppose income increase by 50% for each person a) Draw BILL'S income-offer and Engel curves for both goods