Please answer parts 1-4 in the below question :

Suppose we are interested in the above topic. and wish to first establish the theoretical linkage between fast food consumption and weight outcome. Consider to formulate the consumer's problem as: maxU(W(F, H],F,H, C] W: weight F: fastfood consumption H: healthy food consumption C: other consumption which is to be maximized under the budget constraint: PfF+PhH+PCC=I where Pf, Ph and R: are price offast foods, healthy foods and other consumption items, respectively, and income I is treated as given. Consider the fastfood tax in terms of fast food price change. 1} Solve for the optimal weight outcome as a function of exogenous variables. 2} It is then clear that the partial derivative 6W\" /6PF is of our primary interest. From its expression, show that wpf = ewpe-p', + EWHEHPf, where a\" denotes the elasticity between X and Y. 3} What signs do you expect from EWF and 511.3? 4} Briefly explain how you will design a survey to get data and empirically estimate epf