3. Given the following information; solve the consumer's problem by finding the optimal demand functions for H and T: U(X.Y)=X1 2?\" Also, you are given the the following initial market conditions: Rt=$5 e-=$5 M28100 a. Setup the Optimization Problem b. Find the First Order Conditions of ptimiaation c. Find 3-? and if" d. Graph the solution and explain the economic intuition behind the graph: i.e. 1What are the conditions met at the optimal bundle? Introduce another consumption bundle and explain why.r it is NDTthe optimal. e. If income doubles, what will the newr F and 'f* be? f. If'your preferences change and 't' becomes preferred to X; illustrate howr the consumer's optimization problem might change, and solve for the new X\" and W\" under your new model