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.

(a) Develop a model to help Lynch determine which carrier it should hire to make its deliveries. Provide a table summarizing how many truckloads will be sent to each city by each carrier.

(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?

(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.

(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.

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\begin{tabular}{|l|l|l|l|l|l|l|} \hline City & Carrier 1 & Carrier 2 & Carrier 3 & Carrier 4 & Carrier 5 & Truckloadsdemanded \\ \hline 1 & $670 & & 1210 & & 1213 & 30 \\ \hline 2 & & & 810 & 1315 & 913 & 20 \\ \hline 3 & & 555 & 910 & 1115 & 713 & 10 \\ \hline 4 & & 755 & 1510 & 715 & & 25 \\ \hline 5 & 770 & 655 & & 615 & & 35 \\ \hline \end{tabular}