A profit-maximizing firm manufactures widgets (Y) using machines (K) and full-time
workers (L). In any given week, its output is given by the production function:
Y= F (K, L) = 1200K +700L + 2KL - L2 - 2K2
The marginal product of labor (MPL) is
MPL = 700 +2K - 2L
And the marginal product of capital (MPK) is
MPK = 1200 +2L - 4K

The firm operates in perfectly competitive market and product markets. The going price of capital (r) is $1,000 per machine per week. Moreover, the firm sells its output at the going price (p) of $1 per widget. Consider the firm's short run labor demand problem.

If the current stock of capital is fixed at 250 units, how many full-time workers should the firm employ if the weekly salary of each full-time worker (w) is $400 per week? Compute the firm's level of output and profits per week in this short-run equilibrium.