A coffee shop has two warehouses to deliver coffee beans across the US. One warehouse is in Seattle (SE) and the other one is in New York (NY). Both warehouses have a roasting capacity of 1500 lb of coffee beans each every day. Three major customers, one in DC, one in Dallas (DA) and one in Los Angeles (LA), regularly order coffee beans online. The customer in DC orders 1000 lb, the one in DA orders 1500 lb, and the one in LA orders 500 lb of coffee beans every day. The following network shows the costs and capacities on each route that can be used to deliver these orders. SE 1100 750 (LA) 1500 1300 500 2000 250 -500 400 DE 300 2600 1400 400 2000 700 1000 780 900 400 100 DA En CH 1500 800 800 1300 900 -1500 (NY) 200 DC 900 -1000 The numbers on the edges shown in black are the distances [in mi] between each node (i.e., costs) and the numbers in red are the capacities [in lb]. a) [15pt] Formulate a linear programming problem to find the delivery strategy with minimum cost over this network. Report the cost and capacity matrices and the flow constraints on each node. b) [15pt] Solve the linear programming problem defined in part a) using Excel's solver. Report the final objective value and the delivery amounts on the network at the optimum.