Bill shares a dormitory room on the UTech campus. The dormitory offers soft drink and chips for sale in vending machines. His utility function is as follows

Bill's Utility function U(S,C)= S^0.3C^0.7

Where S is the number of soft drinks per week and C the number of bags of chips per week

1. Use the Lagrange method to derive Bill's demand functions for soft drink and chips.

(8 marks)

1. If soft drink is priced at $100 each, chips $50 per bag and Bill has $5000 per week to spend on chips and soft drink,

1. How many of soft drinkand chips should BILL purchase per week respectively?

(4 marks)

1. calculate the utility level BILL, received at the optimal bundle found in part B(i)

(6 marks)

1. Suppose Bill consumes 45 units of soft drink and 210 units of chips what would be the income level of the consumer?

(4marks)

1. At the new income level (calculated in part c), illustrate the income-consumption curves and Engel curves.

(8 marks)