Question 5 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 50 units per week from each factory to a Distribution Centre (DC) if needed, and from this DC up to 50 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. DC Warehouse 1 Warehouse 2 Factory From Output Factory 1 transport 7 80 costs Factory 2 transport 70 costs 3 4 9 2 4 Distribution center transport costs 60 90 Units Required at Warehouse a. Formulate the linear program that would be needed to solve this problem. b. Obtain a valid solution to this problem (guess and test is fine) c. Attempt to give some estimated measure of how good you think your solution is compared to what you think is a reasonable estimation of the optimum