A NGO is concerned about a possible need to provide humanitarian aid to a country at risk of hurricane damage and so is planning a program of emergency aid to that country. They are keen to do this at minimal cost. The options are either to deliver the emergency supplies and medical 1 staff using airplanes or helicopters, or a mix of the two. However they only have 6 airplanes and 10 helicopters available to use for this purpose. The costs, capacities (for supplies and staff) and the maximum number available of each aircraft type are shown in the following table:
Plane Helicopter
Cost per aircraft $20,000 $5,000
Capacity for supplies (tons) 200 17
Capacity for medical staff 10 20
Number available 6 10
In the event of a hurricane the country would require 1000 tons of medical aid and 200 staff.
(a) Formulate this problem as an integer program using notation. Clearly identify the sets, parameters and decision variables. Also, describe the objective function and each of the constraints in words as well as math.
(b) Write out the problem instance using the data given.
(c) Use Excel Solver to find the optimal solution and cost.