Question
The boardwalk on the Paradise City beach is 4 miles long with mile markers at 0, 1, 2, 3, and 4 miles, There are 100 customers at each mile marker and each customer's demand for ice cream is given by the function: D = 24 - 4d, where d = distance between customer and nearest ice cream vendor.
There are two ice cream vendors (A and B) and they are currently located at mile markers 1 and 2 as shown above.
a. Find out the demand at each vendor and total demand for the system.
b. Are these the best locations of the vendors from the system's point of view? If not, suggest better locations for the vendors. What is the total system demand now?
c. Compute how much and to whom an incentive should be offered so that the vendors relocate to the optimal locations from the system's point of view? (Assume one unit of ice cream generates $1.50 in profit.)