Please solve this question by use Lagrange multiplier method

3. (A word of warning: you can make your answer complicated or you can think about this for a bit and simplify things a lot.) Once a week, Steffen's mom lets him eat fast food. Steffen likes pizza (P) and soda (S) and spends all the money his mom lets him on those two items. Steffen's preferences are described by the utility unction U (P, S) : e'/PS. a. If pizza costs $2.50 per slice and soda costs $1.00 per cup, how much pizza and soda will Steffen buy if his mom gives him $10.00 to spend? b. Research shows that soda consumption increases obesity in children, so the fast food restaurant tries to discourage soda consumption by increasing its price for soda to $4.00 per cup. However, Steffen's mom only lets him drink soda once a week and is ne with letting him drink all the soda he wants then. How much more money would Steffen's mom have to give him in order for him to get the same utility he did before the price hike