Question

1. Transportation costs per ton of product vary with distance.

For turcks the function is: TC_t= 2+1.5d

For rail it is: TC_r=4+d

For barge it is: TC_b=6+.75d

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 of d = 1, 2, ...,10. Graph the problem and label the modal break points clearly.

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2. Farmers growing peas ship them to the processing plant of their cooperative. The price paid for peas by the coop is $30 per ton minus the cost of haulage. The coop charges hauling fees of: TC_c = 1+d

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 of distance from the plant.

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3. These same farmers buy fertilizer from the coop at $10/ton. The fertilizer store is at the same location as the processing plant for the peas. They pay for haulage from that location at a cost of: TC_f = 2+d

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 at d = 1, 2, ...,10 miles of distance from the plant.

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4. Suppose that a farmer uses 1 ton of fertilizer to produce 3 tons of peas. Prepare a table to show the net revenue that farmers would receive from selling 3 tons of peas to the coop and buying 1 ton of fertilizer from the coop for locations at a distance of d = 1, 2, ..., 10 miles from the location of the cooperative.

[Insert an image of your graph here]

Answer 1