Hello, please help me solve this problem while showing the steps

2. Consider the food stamp programs in the US.under this program, poor households receive a certain quantity of \"food stamps\"stamps that contain a dollar value which is accepted like cash for food purchases at grocery stores. Let good 1 be food and good 2 be dollars spent on everything else. Suppose this household's tastes for spending on food, :31, and spending on other goods, :52, can be characterized by the utility function other goods can be characterized by the utility function u(3:1, 11:2) = alnx1+lnx2 (a) (1 point) Calculate the level of food and other good purchases as a function of Y and the price of food 391. For the rest of this exercise assume that the household has income $1500 and p1 = 1. (b) {2 points) What is the range of athat makes the $500 food stamp program equivalent to a cash gift of $500? For the remainder of problems, further assume that a = 0.5. (c) (I point) Instead of food stamps, the government tells this household that it will reimburse 50% of the household's food bills. HOW much food will this household buy under this alternate policy? ((1) (1 point) How much does this policy in (0) cost the government for this household? Call this amount S. (e) (2 points) How much food will the household buy if the government gives S as a cash payment and abolishes the alternate food subsidy program? (f) (2 points) Determine which policy the price subsidy that leads to an amount 3 being given to the household, or the equally costly cash payment in part (c) is preferred by the household