It is often important to understand how the optimal number of facilities and their locations depend on the relative values of the fixed facility location costs and the transport costs. This is...

It is often important to understand how the optimal number of facilities and their locations depend on the relative values of the fixed facility location costs and the transport costs. This is particularly important if the cost factors that affect the cost per unit distance (e.g., driver wages, fuel costs, and vehicle acquisition and maintenance costs) change.

(a) For the network of Exercise 7.5, find the cost per mile (accurate to the nearest hundredth of a unit) at which the optimal number of facilities becomes one less than the optimal number found in Exercise 7.5. Where do you locate facilities now? How many do you locate?

(b) Repeat part (a) until you find the cost per mile at which it is optimal to locate only one facility. For each range of the cost per mile in which the number of facilities remains constant, how many facilities do you locate? Where should the facilities be located? Within each range of the cost per mile, do the facility locations change? (Be careful when you consider the case in which you locate only one facility.)

(c) For the cost per mile varying between 0 and 1, plot the following quantities versus the cost per mile:

i. the total cost

ii. the fixed facility location costs

iii. the transport costs