please solve with explanations.

Question 1 Fun with price indices. Suppose that your utility function over health care (h) and other goods (c) is given by U(h, c) and that you have a fixed income of $100. Also assume that the indifference curves of your utility function have the usual convex shape. Each year, you choose h and c to maximize your utility subject to a budget constraint: puh + pec = Y where, pa is the price of health care, p, is the price of other goods, and Y is your income. In year 1, the price of health care is $1, while the price of other goods is $2. At these prices, you demand 30 units of health care and 35 units of other goods. In year 2, your utility function and your income do not change, but prices do. Health care becomes more expensive at $1.50, while other goods become cheaper at $1.50. At these prices, you demand 20 units of health care. (a) Assuming you spend all your income in year 2, how many units of other goods do you buy [you may purchase a fractional number goods]? (b) Draw a graph with your demand for health care on the x-axis and your demand for other goods on the y-axis. On this graph, draw your budget constraints in year 1 and in year 2 [2 different budget constraints]. On these budget lines, indicate your demand points for h and c in year 1 and year 2. Also draw indifference curves tangent to the points in year 1 and year 2 that represent your demand. Label the indifference curves U, and U2.(c) Do the price changes leave you better off, worse off, or the same as before? (e) Calculate the Laspeyeres price index; that is, the amount of money you need to buy the Year 1 bundle in Year 2 (with Year 2 prices), divided by the money you paid for it in Year 1