18. SuperCity is a large retailer of electronics and appliances. The store sells three different

models of TVs that are ordered from different manufacturers. The demands, costs, and

storage requirements for each model are summarized in the following table:

It costs $60 to do the administrative work associated with preparing, processing,

and receiving orders, and SuperCity assumes a 25% annual carrying cost for all

items it holds in inventory. There are 3,000 square feet of total warehouse space

available for storing these items, and the store never wants to have more than

$45,000 invested in inventory for these items. The manager of this store wants to

determine the optimal order quantity for each model of TV.

Question 1: Formulate an NLP model for this problem.

Question 2: What is the value of the objective function (cost) at the optimal solution? Do not include the cost of purchasing the items in the total cost function (just include ordering and holding costs).

Annual Demand Unit Cost Storage space req'd Model 1 800 $300 9 sq ft Model 2 500 $1,100 25 sq ft Model 3 1,500 $600 16 sq ft Annual Demand Unit Cost Storage space req'd Model 1 800 $300 9 sq ft Model 2 500 $1,100 25 sq ft Model 3 1,500 $600 16 sq ft