Derive the labor demand functions that are associated with the two production functions given below. The level of output is denoted by q. The two inputs are labor (h) and capital (k). You should derive the function that relates the level of labor utilized at each possible output level, q > 0. We will assume that the price per unit of capital is r = 1, that the wage rate is w = 2.

(a) min{2h, 3k}

(b) max{3h,k}