Josiah's Jets builds small jet aircraft to sell to major corporations for executive use. To meet the needs of these executives, Josiah's custom designs each fleet of jets that its clients purchase. Custom designing the jets incurs a substantial set up cost in order to create logos and initiate production of a client's fleet. Josiah's Jets has recently received requests from four potential new customers, but because of some shorter than normal deadlines and a relatively heavy workload due to previously accepted contracts, they will not be able to fill all four of these client requests. Therefore, a decision needs to be made now on the exact number of jets Josiah's Jets can agree to produce (if any) for each of the four potential clients. Because of its stature as a price leader, it is assumed that Josiah can convince each of the new clients to allow them to produce either their entire fleet, or any subset of that fleet. The production manager at Josiah's Jets has indicated that the company has the capacity to build a total of at most 16 planes to accommodate these new clients. Relevant data are given in the table below. The first row indicates the one time set up costs required for beginning production of customized aircraft for each of the new clients, the next two rows show the anticipated selling prices and variable unit production costs for the jets in each client's fleet, and the last row gives the total number of jets that each client intends to purchase for its fleet. Set Up Cost Selling Price Variable Cost Fleet Size Client 1 $50,000 $600,000 $400,000 5 Client 2 $36,000 $750,000 $520,000 8 Client 3 $30,000 $720,000 $500,000 6 Client 4 $40,000 $540,000 $360,000 3 Formulate an Integer Linear Programming model that Josiah's Jets can use to determine the number of jets that they should agree to produce for each of the four new clients so as to maximize their total profit. (NOTE: Profit = Revenue - Total Cost). FS