Please help me! I had worked these problems out myself but I just want to make sure that I am doing it correctly. I am a bit lost that is why. Thank you.

1. (4 points) Consider the following demand and supply relationships in the market for golf balls: O* = 90 2P 2T and O =9 + 5P 2.5R, where T is the price of titanium, a metal used to make golf clubs, and R is the price of rubber. a) If R=2 and T= 10, calculate the equilibrium price and quantity of golf balls. (1 point) b) At the equilibrium values, calculate the price elasticity of demand and the price elasticity of supply. (1 point) c) At the equilibrium values, calculate the cross-price elasticity of demand for golf balls with respect to the price of titanium. What does the sign of this elasticity tell you about whether golf balls and titanium are substitutes or complements? (2 point) 2. (3 points) A consumer has preferences between two goods, hamburgers (measured by H) and milkshakes (measured by M). His preferences over the two goods are represented by the utility function U =H + VM. For this utility function MU = 1(2VH) and MU = 1(2NM). a) Determine if there is a diminishing MRSj,y for this utility function. (1 point) b) The consumer has an income of $24 per week. The price of a hamburger is $2 and the price of a milkshake is $1. How many milkshakes and hamburgers will he buy each week if he maximizes utility? (2 points) 3. (3 points) Helen's preferences over CDs (C) and sandwiches (S) are given by U(S, C) = SC + 10(S + C), with MUc= $+ 10 and MUs = C + 10. If the price of a CD is $9 and the price ofa sandwich is $3, and Helen can spend a combined total of $30 each day on these goods, find Helen's optimal consumption basket. 4. (10 points) Carina buys two goods, food F and clothing C, with the utility function U = FC + F. Her marginal utility of food is MUr = C + 1 and her marginal utility of clothing is MUc = F. She has an income of 20. The price of clothing is 4. a) Derive the equation representing Carina's demand for food. (4 points) b) Determine the numerical size of the income and substitution effects when the price of food increases from | to 4. (6 points)