Q. 1. Lee has the utility function U(x1, x2) = (x1+1)(x2+4) The price of x2 is $1. Lee spends all his income to buy 6 units of x2 also no x1. Illustrate what is the minimum level of the price of x1 compatible with these facts? Explicate your answer.

2. Sheila budgets $9 per week for her morning coffee with milk. She likes it only if it is prepared with 4 parts of coffee and 1 part milk. Coffee costs $1 per ounce and milk costs $0.5 per ounce. How much coffee and how much milk will Sheila buy per week? How would your answer change if the price of coffee rises to $2 per week? Illustrate your answers graphically.

3. Max has the utility function U(x1,x2) = x1(x2+2)

(a) If the price of x1 is 2, the price of x2 is 1, and Max's income is 10, how much x1 will Max consume? How much x2?

(b) Suppose that Max's income level is 10. Derive Max's demand function for x1. Is x2 a substitute of x1 or a complement of it? (Be sure to show your calculations.)