7. Suppose a hospital has the profit function π = (P - MC) * D(Q) – FC(Q) where P is the payment to the hospital for treating one patient, MC is

the marginal cost of treating one patient, D(Q) is the number of patients the hospital receives (demand) when it chooses quality level Q and FC(Q) is the fixed quality investment cost of choosing quality level Q. Firms choose Q to maximize profit. Let P = 6, MC = 3, D(Q) = 1 + 2Q, FC(Q) = Q². Find the first order condition of this maximization problem. (HINT: Take the partial derivative of with respect to Q and set that equal to 0.)