Consider the following utility functions(i)U(x1; x2) =x2+ Inx1(ii)U(x1; x2) = 10x2=31x3=42+ 23:7a. Derive the demand function forxlandx2.b. Graphically illustrate the demand and Engel curves for commodityx2.2. Consider the following utility functions.(i)U= min(x1;4x2)(ii)U(x1; x2) = 5x1+ 3x2(iii)U=x1x2=(x1+x2)(iv)U= 8x31x2a. Drive the demand function forx1andx2as functions ofp1 ,p2andl.b. Determine whether the demand functions are downward sloping.c. Are the commodities normal or inferior? Explain.3. Each day Ryan eats lunch at school. He only eats Twinkies(t)and soda(s). Ryanísutility function for these two commodities is represented byU(t; s )=pts: (a) If Twinkies cost$0:10each and soda costs$0:25per cup, how will Ryan maximizehis utility with the $1:00his mother gives him?(b) If the school tries to discourage Twinkies consumption by raising the price to$0:40, by how much will Ryanís mother have to increase his lunch allowance toprovide him with the same level of utility he received in part(a)?1