Problem 1 Lynch Foods , located in Toronto produces soup , syrups and jams but outsources the delivery of its products to third party carriers. Lynch ships products to 5 cities and have ask 5 carriers to bid on its business. The resulting bid, $/truckload is shown. Each carrier can make deliveries to some cities but not all the cities. The monthly demand at each city and the cost of each carrier to deliver one truck load is shown. Finally, carriers 1 and 2 demands that Lynch pays them a minimum monthly retainer of $270 and $150 respectively, in the event they are hired. City Carrier 1 Carer 2 Carrier 3 Carer 4 Carrier 5 Truckloads demanded 3670 1210 1213 30 913 20 565 111 7013 755 1510 715 25 5 770 655 615 35 (a) Develop a model to help Lynch determine which carrier it should hire to make its deliveries . Solve the model using LINGO . Provide a table summarizing how many truckloads will be sent to each city by each carrier . Attached LINGO code and output (10 marks) (b) Dealing with too many carriers can be cumbersome . Suppose Lynch Foods wants to give its business to 2 carriers , which 2 carriers would it be? What is the percent increase in cost for Lynch? (5 marks ) (c) Considering the original problem in (a). What changes would you need to make to the model if Carrier 3 will agree to make deliveries for Lynch only if it gets to deliver a minimum of 50 truckloads .(2 marks ) (d) Considering the original problem in (a). What changes would you need to make to the model if Carrier 3 will agree to make deliveries to a city for Lynch if it gets to deliver a minimum of 10 truckloads to that city. (2 marks ] Problem 2 As treasurer of the school PTA , you chair the committee to decide how the $20,000 raised by candy sales will be spent . Four kinds of projects have been proposed , and facts on each are shown below . Assume that the variables do not have to be integers Number Volunteers Needed Project Requested Unit Cost (Person - days , each ) Basketball goals $400 Encyclopedia sets 750 in wok Field trips 300 Computer Stations 800 (a) Develop a goal programming model that would represent these goals and priorities . (8 marks )