A firm produces widgets, and uses $k$ and $l$ as inputs. They have the production function $f(k, l) = k^{1/2}l^{1/2}$, and the costs of capital and labor are $v = 1$ and $w = 1$, respectively. Their goal is to minimize costs for a given level of output $q$.
What are the contingent factor demands for capital and labor?
(a) $(k_c, l_c) = (2q, 2q)$
(b) $(k_c, l_c) = (q, q)$
(c) $(k_c, l_c) = (q^2, q^2)$
(d) $(k_c, l_c) = (2q^{1/2}, 2q^2)$