Coffee shops are planned to be placed on the second floor of one of the four office buildings. The office tenants are located at P1(20,70), P2(30,40), P3(90,30) and P4(50,100) in 2D plain. 50 persons per day are expected to visit the first office, 30 the second office, 70 the third office and 60 the last office. 70% of visitors are expected to drop by the coffee shop. Each unit distance which a customer has to travel costs the owner of the coffee shops the loss of $0.25 in revenue. The installation cost of shops is $5000. The objective function is to minimize total weighted cost. 1. Please draw 2D map, which shows all the locations of four offices.
2. Assume that you will have "p" number of coffee shops. Please model this problem using the optimization (Integer Programming) model
3. If p = 1, where will be the optimal location?
4. If p = 2, where will be two optimal locations?
5. Assume that now the installation cost of shops goes down, $1000. If you were a manager, will you launch two coffees shops or one coffee shop? Explain.