(Please explain a little more detail, Thanks)

Consider Gaby's utility function u(X1, X2 ) = 4x1 + x2, where x1 is the consumption of rice and x2 is "everything else". Assuming the income is m and the prices are p1 and p2, repectively.

1 ) Is this preference homothetic? Justify your answer.

2) Derive the ordinary demand function for both x1 and x2 .(Consider all possible situations)

3) Suppose m = 30, p1 = 1, and p2 = 2, compute her optimal consumption bundle.

4) Now it cost p'1 = 4 to buy a unit of rice, what is his new consumption bundle?

5) Draw Engel curves for both x1 and x2.