BRAD lives in a dormitory room on the UTech campus. The dormitory offers soft drink and chips for sale in vending machines. He consistently chooses between soft drink and soda to maximize his satisfaction given the utility function, income and the prices of soda and chips. The table below shows Bill's utility function and income

Customer	Utility Function	Income
Bill	U(S,C)= S0.3C0.7	$12,000

Given S is the number of soft drinks per week and C the number of bags of chips per week. Answer the following

Derive the demand functions for soft drink and chips for BILL.

(12 marks)

If soft drink is priced at $10 each, chips $5 per bag per week to spend on chips and soft drink, Calculate the optimal amount of soft drink (S*) and chips (C*) and utility value (U*) for Bill?

(6 marks)

Suppose income increase by 100% for each person Draw BILL'S income-offer and Engel curves for both goods.

(9 marks)

Suppose the price of chips increase from $5 to $10 and income remain constant at $12000 draw BILL'S price offer curve and demand curve.