Minimum price P = ?

A firm's short-run production function is displayed in the figure below. The firm's variable input is labor. Assume that when 4 units of labor are being used, the slope of the short-run production function reaches its maximum value of 7 (27 = 7 when L = 4). If 6 units of labor are being used, the slope of the production function is 3 ( 27 = 3 when L = 6). Finally, the slope of the production function is equal to 5 when five units of labor are used (27 = 5 when L = 5). Suppose the firm has to pay a wage of $12 (w = 12 ) for each unit of labor. What is the lowest the price (p) could be if the firm is maximizing profits in the short-run by producing a strictly positive level of output (q > 0)? 91 18 q (L) 14 8 0 4 5 6