Each week, Mara works l hours per week to consume x1 and x2 quantities of two goods. She has L hours of time at her disposal per week. She choses how many hours she works and the quantities of these two goods she consumes to maximise her weekly utility function given by U(x1, x2, l) = ln(x1) + ln(x2) + (1 )ln(L l),

which is defined for 0 l < L and for x1, x2 > 0. Here and are positive parameters satisfying + < 1. She faces the budget constraint p1x1 + p2x2 = wl, where w is the wage per hour, p1 is the unit price of good 1, and p2 is the unit price of good 2.

b) Assume that is equal to 0.25 and is equal to 0.5 and that Mara has 16 hours at her disposal per day. Mara can buy either one unit of x1 or two units of x2 with the income she generates by working for 4 hours. Find Mara's demands of x 1 and x 2 , and her labor supply l that maximises her weekly utility. [5 points]

pls answer in detail. you must outline what the constraint is which like properly pls!