A manufacturer produces some output called "Product" using a raw material called "Input". To production of 1 ton of Product requires 3/5 ton of Input. The manufacturer has a contract to deliver 50 tons of Product to Store M (Store M is the "market" for Product). Input is available in Spot N (Spot N is the source of Input, equivalent to "mine" in the textbook). Store M is 40 miles away from the Spot N. The shipping cost of both Product and Input are $2 per ton per mile. We will help the manufacturer to find the total transport-cost minimizing factory location. To arrive at the answer, go through the following steps in parts (a), (b) and (c).

However, our manufacturer faces an additional issue. Store M and Spot N are in different countries, making the manufacturer subject to tariffs based on trade agreements between the two countries. The Border is 15 miles from Spot N. The width of the Border is negligible, placing Store M at 25 miles from the Border. The trade agreements are such that Product can be moved between the countries freely but transporting Input across the border involves a payment of $60 per ton in tariffs. Given this additional information, let us help the manufacturer re-calculate his shipping costs. We will go through similar steps as earlier, now following parts (d), (e) and (f).

(d) Now, consider four potential locations for the factory: Spot N, Spot N-side of Border (let's label this location as N-side of Border), Store M-side of Border (label this location as M-side of Border) and Store M. Calculate shipping costs by filling in the cells of the table below. Show your calculations.

1. (e)Again, present a graphical illustration of your calculations. In addition to the previous locations on the x-axis, now mark out N-side of Border and M-side of Border. The y-axis represents shipping costs. Clearly label the axis, all three shipping cost lines and significant points on the graph.
2. (f)In this case, what is the total transport-cost minimizing location for the manufacturer? How do you make intuitive economic sense of this result?