Suppose a hospital only needs one input, nurses, to treat

Suppose a hospital only needs one input, nurses, to treat their patients. A public insurer reimburses each treatment at $10 and suppose that the hospital needs to hire L nurses to provide T = 5L − 1/20 ∗L^2 treatments. Hospitals pay their nurses a wage W and suppose that 5 + W/2 nurses are willing to work at the hospital for a wage W.

Specify the hospital’s demand curve for nurses as well as the nurses’ labor supply curve. Also display them in a diagram, with employment on the horizontal axis and the wage on the vertical axis.