The Good Works General Hospital has a local monopoly in the sale of hospital services in its market area. Its product demand curve is p = 30 - 0.4x, where p is the price of a hospital day and x is the number of hospital days per year at Good Works. Given this demand curve, derive the equation for marginal revenue (MR).

Good Works is the only employer of professional nurses in its market area. It faces a supply of nurse labor of w = 5 + 0.9E, where w is the nurse hourly wage and E is the full-time-equivalent of nurses employed by Good Works. What is the marginal labor cost of nurses? Assume each nurse can monitor four patient rooms per hour (with one patient per room) and Good Works is a profit maximizer. Then how many professional nurses should Good Works employ? At what hourly wage? What price should Good Works charge for a hospital day?