An individual with consistent preferences has a utility function denoted as u(x1, x2) = 4lnx1 + 3x2.

PART 1: Utilizing the tangency approach, can you determine the demand functions for each product for this individual? In layman's terms, can you explain how the budget line formula assists us in identifying the best choice for this individual within the context of the tangency method?

PART2: If the cost of good 1 rises, would the individual opt for a higher, lower, or identical quantity of good 1 as previously? When breaking down the impact of this price shift on the consumer's demand for good 1 using either the Slutsky or Hicks method, can you determine the portion of the demand alteration attributable to the substitution effect versus the income effect? Please justify your responses by referencing the demand equations from part 1.