Consider the production function y=x₁ ^1/3x₂^2/3 where y is units of output, and x₁ and x₂ are units of inputs 1 and 2, respectively.

a)If the unit input factor costs of input 1 and 2 are 1 and 16, respectively, what are the conditional factor demands for each input?

b)What is the long run total cost function for a firm producing using this technology when the factor cost of input 1 is 1 and the factor cost of input 2 is 16?