A farmer produces three types of vegetables (carrots, eggplants, tomatoes) in 3 different farms. Carrots and eggplants grow in the 1st farm, only tomatoes grow in the 2nd farm, and eggplants and tomatoes grow in the 3rd farm. Produced vegetables are first sent to two mediary warehouses, and then are distributed to four outlets in four different cities. Warehouse capacities are 40 and 50 tonnes respectively. In each farm, there are two trucks (one to go to each warehouse), each having a capacity of 10 tonnes of vegetables (regardless of the vegetable type). There are also four trucks in each warehouse (one to go to each city), with 15 tonnes of capacity. The cost (fuel) is assumed to be linearly affected by the amount of load, and also by the distance. The corresponding transportation cost per box between nodes is shown in the Table 1. The sales prices for carrots, eggplants and tomatoes per ton are $2000, $5000, $8000, respectively. The demands for each of them in each city are given in Table 2. The company wants to fulfil as much demand as they can.

The company has an option to replace the trucks operating between farms and warehouses with the ones with 20 tonnes of capacity, at a cost of $10,000 per each truck. Calculate whether replacing all trucks is profitable (Hint: solve the original model, then change the capacities and resolve the model, compare the objective function difference with the cost of replacement.)

Facility 1 Facility 2 Facility 3 City 1 City 2 City 3 City 4 Warehouse 1 850 798 1562 680 1561 865 1772 Warehouse 2 1176 1586 373 1515 471 584 718 Table 1: Transportation cost per box between locations. como en toe.edu City 1 City 2 City 3 City 4 Carrot Eggplant Tomato 9 7 5 7 7 10 12 8 5 9 Table 2: Tonnes of demand for each vegetable in each city Facility 1 Facility 2 Facility 3 City 1 City 2 City 3 City 4 Warehouse 1 850 798 1562 680 1561 865 1772 Warehouse 2 1176 1586 373 1515 471 584 718 Table 1: Transportation cost per box between locations. como en toe.edu City 1 City 2 City 3 City 4 Carrot Eggplant Tomato 9 7 5 7 7 10 12 8 5 9 Table 2: Tonnes of demand for each vegetable in each city