A firm production function is given by q = f(k,l) = kl. q₀= 100. w = $20, v = $5. At the point at which this firm minimizes the cost of producing q_0:

1. find the units of labor (l) and capitol (k)
2. determine the value of the Lagrange multiplier lambda at the cost minimizing input choice
3. The demand equation for capital input k, in terms of q, w, and v, is given by the equation: k* = [q(w/v)]^n. Solve for [n].