Suppose that a business has 3 retail locations along a highway: one that is 10 miles from
Question:
Suppose that a business has 3 retail locations along a highway: one that is 10 miles from the start of the highway, another that is 30 miles from the start of the highway, and the last is 80 miles from the start of the highway. Each needs a full truckload of goods each day. The business wants to locate a warehouse somewhere along the highway.
i) what location along the highway would minimize the total amount of truck miles driven?
ii) Suppose that for some strange reason, the cost of driving a truck “m” miles was m^2 dollars instead of just m dollars. Then, what would be the best location along the highway to put the warehouse, to minimize total trucking cost?
iii) How do your answers in (i) and (ii) relate to the mean and the median of 10, 30, and 80?
iv) Repeat part (i) but in the situation where the company has 4 retail locations: at positions 10, 30, 70, and 80.
v) Repeat part (ii) but in the situation where the company has 4 retail locations: at positions 10, 30, 70, and 80.
vi) is your observation in (iii) still true?