A simple transportation network is shown in the figure below. Both factories 1 and 2 are producing a certain product to supply for warehouses 1, 2 and 3. The arrows represent the transporting path between factories and warehouses and the numbers on the arrows represent the cost of shipping each unit product on that path. For example, from factory 1 to warehouse 3, the cost of shipping is $6/unit. The supply capacities of factory 1 & 2 are 80 and 70 units respectively, and demand requirements of warehouse 1, 2 and 3 are 40, 50 and 60 units respectively, as shown in the figure. For example, factory 1 is capable of producing 80 units and warehouse 1 needs at least 40 units. Please construct a linear programming model to minimize the shipping cost based on the information above. (Assume that A, B, and C indicate the quantities shipped from Factory 1 to Warehouse 1, 2, and 3 respectively; D, E, and F indicate the quantities shipped from Factory 2 to Warehouse 1, 2, and 3 respectively)

Which of the following is the objective function?

Question 12 options:

	maximize ($4*A+$5*B+$6*C+$4*D+$5*E+$6*F)
	minimize ($5*A+$6*B+$4*C+$7*D+$4*E+$6*F)
	minimize ($4*A+$5*B+$6*C+$4*D+$5*E+$6*F)
	maximize ($5*A+$6*B+$4*C+$7*D+$4*E+$6*F)