A system for printer manufacturing consists of a number of factories, warehouses, distribution centers, and customers as shown in Figure 1. Printers Type "Laser Jet Pro" are fabricated in two (2) factories located at different cities. The printers are then shipped to two (2) warehouses at which they then shipped to three (3) distribution centers. At the distribution centers, printers are subjected to a very strict quality inspection process. Any printers do not meet quality standards will be returned directly to the factories to be reworked (repaired). The printers passed the inspection test are transported to ten (6) customers to satisfy their needs. From historical data, the rate of rework is (2% of the printers inspected at distribution centers). The unit transportation cost between ant two nodes in the network is estimated to be SR 5. Factories Warehouses Figure 1: Printer manufacturing and distribution network Factory Daily Production Capacity (printers) Production cost(SR/printer) Rework cost(SR/printer) The two factories have production capacities and production cost listed in the following table. Distribution Centers Daily demand FI 950 100 10 Customers F2 800 95 10 The warehouses have a limited space (volume shown in table below).Each printer has the following dimensions (50 cm length, 40 cm wide, and 20 cm height). Warehouse WI W2 Volume (m^3) 400 350 Customer daily demands need to be satisfied without any shortage (table below). Customers C1 C2 C3 C4 C5 C6 120 180 144 150 175 200 Develop a mathematical model (in general form) to help the company determine the number of printers to produce in each factory, flow between each two nodes, number of printers returned per day while minimizing the total cost including (production cost, rework cost, and transportation cost). Find the optimal solution using software