A company maintains inventories of its 5 prod ucts, replenishing the stock of an item whenever it reaches zero by manufacturing a fixed lot size of new units. The following table shows the setup cost for manufacturing, the unit volume, the unit annual inventory holding cost, and the estimated annual demand for each item.

Product 1 2 3 4 5 Setup 300 120 440 190 80 Volume 33 10 12 15 26 Holding 87 95 27 36 135 Demand 800 2000 250 900 1350 Managers wish to choose lot sizes for each item that minimize total average annual setup and holding costs while assuring that the maximum combined stored volume will not exceed the 4000 cubic meters available. Assume that lots arrive the instant they are ordered.

(a) Formulate this operations problem as a constrained NLP. (Hint: What is the average on hand inventory of item j as a function of the lot size for j?)

(b) Use class optimization software to start from a feasible solution and compute at least a local optimum.