Solve the question plz

A consumer has the following preferences \"(11'le =103(I1)+ 9:2 Suppose the price of good 1 is p1 and the price of good 2 is m. The conSumeI' has income m. (a) Find the optimal choices for the utility maximization problem in terms of p111); and m. Denote the Lagrange multiplier by A. (b) How do the optimal choices change as or increases? What does the income offer curve (also called the income expansion path) look like for this consumer? (You can show it on a diagram.) (c) What is the slope of the Marshallian demand curve for good 1? Use the Slutsky equation to nd the slope of the Hicksian demand curve for good 1, without actually solving the expenditure minimization problem. (d) For a utility level it, solve the expenditure minimization problem and nd the optimal choices in terms of pl, 1): and . Denote the Lagrange multiplier by pi. (c) Find the Hicksian demand curve for good 1. What is the slope of this curve? Does it match your answer in (c)? (f) Find the expenditure function. Find its partial derivative with respect to 3);. Provide an interpretation of this derivative in terms of choice behavior. (g) Use the answer in (e) to nd compensating variation for a change in P1 from a to b, (I