Question on utility function

Question

 Assume a consumer with the given utility function: U = 3y₁y₂ + 5.

1. Suppose y₂ = 1, derive the marginal utility schedule for y₁. In what direction is it moving?
2. Obtain indifference curves for U = 23 and for U = 59.
3. Suppose money income = $18.00, p₁ = $6.00, and p₂ = $2.00, determine the consumer equilibrium position by using the above indifference curves.
4. Suppose money income = $18.00, p₁ = $2.00, and p₂ = $2.00, determine the consumer equilibrium position by using the above indifference curves.
5. Employing the results of (3) and (4):                                                                                                                                                             
   
   • How much was the rise in demand for good 1 caused by the substitution effect? How much was caused by the income effect?
   • Draw the consumer demand curve for good 1
   • Find out whether goods 1 and 2 are substitutes, complements, or independents.
   • Derive the price elasticity of demand and define whether it is elastic, inelastic, or unitary elastic.
   • Suppose that money income rise from $18.00 to $30.00 while prices remain constant at p₁ = $6.00 and  p₂ = $2.00. Determine the new consumer equilibrium position. By using the results just obtained, classify goods 1 and 2 according to whether they are superior, normal, or inferior goods.