Question 1(50%) A contractor, Susan Meyer, has to haul gravel to three building sites. She can purchase as much as 18 tons at a gravel pit in the north of the city (pit 1) and 14 tons at one in the south (pit 2). She needs 10, 5, and 10 tons at sites 1, 2, and 3, respectively. The purchase price per ton at each gravel pit and the hauling cost per ton are given in the table below. (a) Susan wishes to determine how much to haul from each pit to each site to minimize the total cost for purchasing and hauling gravel. Formulate a Binary/Pure/Mixed Integer Linear Programming Model for this problem. Specify a lower bound for each big- M constant, if any. Show all steps clearly. (Note: No need to solve the problem.) (b) Susan now needs to hire the trucks (and their drivers) to do the hauling. Each truck can only be used to haul gravel from a single pit to a single site. In additional to the hauling and gavel costs specified in the above table, there now is a fixed cost of $150 associated with hiring each truck. A truck can haul 5 tons, but it is not required to go full. For each combination of pit and site, there are now two decisions to be made: the number of trucks to be used and the amount of gravel to be hauled. Formulate a Binary/Pure/Mixed Integer Linear Programming Model for this problem. Specify a lower bound for each big- M constant, if any. Show all steps clearly. (Note: No need to solve the problem.)