A paper firms short-run Cobb-Douglas production function is q = ALK, where K is the fixed amount

A paper firm’s short-run Cobb-Douglas production function is q = ALαKβ, where K is the fixed amount of capital. What is its short-run labor demand function? The estimated Cobb-Douglas production function for the paper firm is3 q = L0.6K 0.2. (15.2)

That is, A = 1, α = 0.6, and β = 0.2. In the short-run, the firm’s capital is fixed at K = 32. The price of a unit of paper is p = 50. What is the paper firm’s short-run production function and labor demand function? How many workers does the firm hire if the wage is w = 15?