A drug company has a monopoly on a new patented medicine. The product can be made in either of two plants. The total costs of production for the two plants are given by c1(y1) = 20y1 + y1^2 and c2(y2) = 10(y2^2) + 5/2(y2^2). The firm's estimate of the inverse demand function for the product is given by p(y1 + y2) = 20 - 3(y1 + y2).
Set up the multiple plant monopolist's profit maximization problem and derive the FONC.