a. John has $100 that he can spend on milk and gas. A gallon of milk costs $5. However, government gives its citizens a coupon that entitles people to 20% discount on their first 10 gallon milk purchases. Gas costs $4 per gallon and government charges $1 for each gallon of purchased gas. John’s utility function is U(x, y) = 9x+10y, where x and y represent gallons of milk and gas consumed, respectively. What is John’s optimal consumption of milk and gas?

b. If government removes the quantity restriction to which the coupon applies (i.e. 20% discount is applied to any quantity of milk purchased), what will be John’s optimal consumption?