Consider a consumer with utility function U$($x$,$ y$)=2$xy$.$ Her income is I $=15,$ and prices are given by px $=2,$ and py $=3.$ Address the following questions: a$)$ Find the demand functions. b$)$ Find the optimal bundle. c$)$ Find the price elasticity of good y Assume the price of good x increases up to px $=3.$ d$)$ Find the income effect, the substitution effect and the total effect. e$)$ Determine whether the good x is normal or inferior f$)$ Determine whether the good x is a Giffen good g$)$ Are goods x and y substitutes, complements, or independent goods?