Consider a firm with the following production function:

f(x1,x2) = 4*x1^(1/2)*x2^(1/2)

where x₁and x₂are the two inputs.

Q1) If the current input level isx₂=10 and the output price is $13 and the price of x1 is $10, then how many units the profit-maximizing level of x₁is?

Q2) If the current input levels are x₁=13 and x₂=7, the marginal rate of technical substitution is ?

Q3) The firm wants to produce 60 units of the output. The price of x₁=$3 and the price of x₂=12. Then how many unit the cost-minimizing level of x₁is?