Consider the utility function u(x₁,x₂) = 2lnx₁ + lnx₂. Initially, the prices are p₁ = $2 and p₂ = $1 per unit. The consumer has an income of $18. Then, the price of good x₁ increases to p'₁ = $3 per unit. (Provide detailed answers for the following parts)

a. State the consumer's maximization problem and use this problem to derive his demand functions for the two goods.

b. Determine whether the two goods are ordinary or Giffen.

c. Determine whether the demand functions for the two goods are elastic, inelastic or unit elastic.

d. Calculate the income elasticities for the two goods. Are they normal? Are they luxuries or necessaries? Justify your answers.

e. Find his optimal consumption bundle and his utility level (round your answers to two decimal places) before and after the price change.

f. Calculate the compensating variation and equivalent variation of the price change (round your answers to two decimal places). What is the relationship between compensating variation and equivalent variation?