(10 points) Develop the algebraic model. Define the decision variables, identify the objective function, and identify all of the constraints.

The exercise is going to be 4 weeks long in the mountains of North Carolina. You have been asked to set up a staging base that the executing units can draw their supplies from. As the sizes of the units participating vary for week to week so do their requirements. The nature of the exercise requires that once each unit departs the staging base they will not return until the end of their maneuvers at the end of the week, as such all of their supplies must be on hand at the start of the week. The two closes bases for you to draw support from are Ft Bragg and Ft Jackson. As each of these bases have their own missions, the capacity they can provide you is limited Atlanta Savannah Supply limit week 1: 700 tons 600 tons Supply limit week 2: 600 tons 800 tons Supply limit week 3: 500 tons 400 tons Supply limit week 4: 600 tons 500 tons You have been assigned a limited number of trucks to transport your supplies. You have been allocated ten trucks with a 34 ton capacity, fifteen trucks with an 18 ton capacity, and twelve trucks with an 11 ton capacity. Due to maintenance requirements each of these trucks can make a maximum of 2 trips a week. As they have different fuel consumption rates, the cost of using each truck also varies. The dollar cost of sending a truck from the depot to each destination is given below: DESTINATION 34 ton truck 18 ton truck 11 ton truck Atlanta $360 per trip $240 per trip $195 per trip Savannah $600 per trip $390 per trip $330 per trip In order for the military operation to be successful, we need to be able to deliver 1000 tons in week 1,1200 tons in week 2, 1200 tons in week 3, and 1000 tons in week 4. We can deliver more than the required tonnage and hold it to meet the tonnage required in the next week, but the amount held cannot exceed 300 tons. You have been told to minimize the cost of supplying the supplies. 1. (10 points) Develop the algebraic model. Define the decision variables, identify the objective function, and identify all of the constraints