Daily, Claire consumes surprisingly just two items each month; chicken and soda. Now x will represent how much chicken (per pound) and y will represent how much soda ( per can) that Claire is able to consume each month. . The cost of one pound of chicken is represented by the variable px, and the cost of one can of soda is represented by the variable py, Claire's monthly income is represented by the variable M. The two goods preferred by Claire are expressed by the Cobb-Douglas utility function u(x, y) = xy* 2 . (1) Figure out Claire's utility maximization problem then also get the famous Marshallian demand functions for the two goods chicken and soda by using the awesome Lagrange method (2) What is Claire's demand for each of the items at px = $8 and py = $4 and M = $72? What is the highest utility level, U * that Claire can achieve if px = $8, and py = $4, nd M = $72? (3 Acquire Claire's indirect utility function and also get the expenditure function, (4) Acquire Claire's compensated demand function by using | the_duality_between_utility maximization and expenditure minimization problems