A warehousing firm services orders for its 5 products from an automatic storage and retrieval

(ASAR) system, refilling storage from backup areas whenever the ASAR stock of any item reaches zero. The following table shows the weekly demand and the unit volume (cubic feet) for each product.

Product 1 2 3 4 5 Demand 100 25 30 50 200 Volume 2 5 3 7 5 Managers wish to decide how many of each item to accommodate within the 1000 cubic feet of available storage to minimize the total number of refilling operations per week.

(a) Formulate this operations problem as a constrained NLP.

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