How should production be allocated among the five plants in

Question

Allocating Plant Output A firm owns five manufacturing plants that are responsible for the quarterly production of an industrial solvent. The production process exhibits diseconomies of scale. At plant p, the cost of making x thousand pounds of the solvent is approximated by the quadratic function f(x) ¼ (1/cp)x2 . The parameters cp are plant dependent, as shown in the table

P	1	2	3	4	5
cP	3	6	4	8	5

The quarterly volume requirement is 50,000 pounds.

How should production be allocated among the five plants in order to minimize the total cost of meeting the volume requirement?