A company will be producing the same new product at two different factories, and then the product must be shipped to two warehouses. Factory 1 can send an unlimited amount by rail to Warehouse 1 every week but not Warehouse 2, whereas Factory 2 can send an unlimited amount by rail to Warehouse 2 every week but not warehouse 1. However, independent truckers can be used to ship up to 75 units per week from each factory to a Distribution Centre (DC) if needed, and from this DC up to 75 units can be shipped to each warehouse. The shipping cost per unit for each alternative is shown in the following table, along with the amounts that will be produced at the factories and the amounts that are needed at the warehouses. Warehouse 1 Warehouse 2 Factory Output 180 To DC From Factory 1 transport 5 11 costs Factory 2 transport 6 7 170 costs Distribution center 4 6 transport costs Units Required at Warehouse 160 190 a. Sketch out what this network may look like. b. Formulate the linear program that would be needed to solve this problem. c. Obtain a valid solution to this problem (guess and test is fine) d. Estimate what could be a "ballpark" value for a best solution e. Estimate what a very bad/worst solution may be f. Compare your valid solution to your guesses at best and worst performance.