1. a) If a consumer with income m has the utility function U(x₁,x₂)=x₁^1/2x₂^1/4

and p₁=2p₂, what ratio of x₁ to x₂ will the consumer choose?

b What is this consumer's optimal consumption bundle when p₁=10, p₂=5, and m=450?

c What is this consumer's optimal consumption bundle if p₂ rises to 10 while p₁ and m remain unchanged?