How do you work these out ?

Peter's utility from vacations (V) and restaurant meals (R) is given by the function U(V, R) = V 2R. The price of vacations is pV and the price of restaurant meals is pR. in dollars per unit Peter has an income M in dollars. i. Use the Lagrangean approach to find the relationship be- tween the quantity of R chosen by Peter as a function of prices and income. This relationship is called Demand func- tion for R. [10 marks] ii. Calculate the area under the demand function for R when the price pR rises from 50 to 75, given pV = 200 and M = 1500. [5 marks] iii. If PR = 50, pv = 200 and M = 1500, what is the change in the utility if the income rises by 1? [5 marks]