1. Transportation costs per ton of product vary with distance. For trucks the function is: = 3 + 1.25 For rail it is: = 5 + For barge it is: = 6 + 1.1 where d is the distance in hundreds of miles and TC is dollars per ton. Make a table showing the least cost mode of transport for distances d = 1, 2, ...,10. Graph the problem and label the modal break points clearly. No graph paper, max 50% points on assignment. 2. Farmers growing peas ship them to the processing plant of their cooperative. The price paid for peas by the coop is $25 per ton minus the cost of haulage. The coop charges hauling fees of: where d is the distance from the farm to the plant in miles and TC is the cost of haulage per ton. Make a table showing the net price the farmers receive for d = 1, 2, ...,10 miles distance from the plant. 3. These same farmers buy fertilizer from the coop at $11/ton. The fertilizer store is the same location as the processing plant for the peas. They pay for haulage from that location at a cost of: = 1.5 + where d is the distance in miles from the fertilizer store to the farm and TC is the cost per ton. The net cost of fertilizer is $10 plus hauling expenses. Make a table showing the net price that farmers pay for d = 1, 2, ...,10 miles distance from the plant.