Slutsky.Consider a consumer with utility function U $($x$,$ y$)=2$xy$.$ Her income is I $=15,$ andprices 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 yAssume 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 inferiorf$)$ Determine whether the good x is a Giffen goodg$)$ Are goods x and y substitutes, complements, or independent goods?