(4) Miguel works on a tea plantation as a plucker. (If you are wondering how someone named Miguel could be working on a tea plantation, remember that Argentina is the ninth largest exporter of tea in the world!) He gets paid a basic wage - we will call it b - and an extra incentive payment s for every kilo of tea leaves that he plucks. So his total payment w is given by w =b+ sy, where y is the number of kilos of tea that he plucks. Miguel has a utility function given by u(w) = 100 ln w, and his cost of plucking y kilos of tea is given by y. So Miguel's net utility is given by u(w) - y. (a) For any given b and s, show that Miguel will pluck y kilos of tea, where y = 100 provided that b