Question

For many firms, production takes place in two or more differentplants whose operating costs can differ. In this question you willbe asked to set up a multiple plant monopolist optimization modeland economically interpret the marginal condition for optimalproduction. To this end, let p() be the inverse demand functionfacing the multiple plant monopolist, where (derivative of )p(y1 +y2 ) < 0, y1 is the output produced at plant 1, and y2 is theoutput produced at plant 2. Note that there is one good produced bythe multiple plant monopolist, its just that now it is produced attwo different plants. Let c1() and c2() be the total cost functionsfor producing the output at plant 1 and plant 2, respectively,where (derivative of) c(y1) > 0 and (derivative of)
c2(y2) > 0 are assumed to hold.

a)What would be the multiple plant monopolists profit maximizationproblem? and how would I derive the FONC? First Order NecessaryCondition for that problem?


Any help would be appreciated. Even pointers in the rightdirection. Thanks :)