3. (30 points) Suppose that a consumer's utility function for two goods (C and S) is UCX, y) : CD'SSU'S The price ofa candy (C) is $2 per unit and the price ofa soda (S) is $1 per unit. Suppose that the consumer has $30 to spend. a. Set-up the constrained optimization problem of the consumer. b. Use a Wm solve the optimization problem in part (a). How much utility does this combination give her? c. Use the tangency condition of M R565 and % to conrm if the optimal bundle found 5 in b is correct. (1. Plot the utility and budget constraint for this problem at the optimum. e. Check your answer by solving the same problem as an expenditure minimization problem. f. If the price of soda doubles to $2, how much income must Chrissy make to maintain the same level of utility