Please help! This is all the information that's given!

1. In a supply chain, there are three manufacturers (i=1,2,3) and two customers (j=1,2). In order to increase the supply chain surplus, optimal distribution network design is desired. The decisions of how much to manufacture and ship, which manufacturing facilities to keep open or shut-down will be given based on a linear programming optimization model. The table below shows the manufacturing and shipping costs from manufacturing facility i to customer j, demand of customer j, capacity of manufacturing facility i. The fixed cost of keeping three manufacturing facilities open are $150,000, $100,000, and $120,000 respectively. Unit revenue for each product manufactured and shipped is $20. from to Manufacturer 1 Manufacturer 2 Manufacturer 3 Demand i Customer 1 SIO $25 $16 80,000 Customer 2 $15 $27 $19 50.000 Capacity i 100,000 30,000 45,000 a) 10 pts Define decision variables for this problem b) 25 pts Formulate the objective function implicitly (hints using summation sign) and explicitly (hint: should have numbers and variables, no summation sign) to maximize the total profit. c) 25 pts Formulate capacity related constraints implicitly (hint: using summation and for all expressions) and explicitly (hint: numbers and variables, no summation sign) d) 15 pts Formulate demand related constraints implicitly (hint: using summation and for all expressions) and explicitly (hint: numbers and variables, no summation sign) e) 10 pts Write non-negativity and/or binary constraints for decision variables. f) 15 pts Formulate a constraint which will imply having exactly two manufacturing facilities open