The Domino Company sells copying machines in six cities: Boston, New York, Philadelphia, Washington D.C., Providence, and Atlantic City. A major factor in making a sale is Domino's quick service. The annual sales of copiers projected depend on whether a service representative is within 150 miles of a city. The first table below provides the projected annual sales in each city in two conditions: (1) at least one service representative is within 150 miles, and (2) no service representative is within 150 miles.
Each copier costs $500 to produce and sells for $1000. The annual cost per service representative is $80,000. Domino must determine in which of its markets to base a service representative. Only Boston, New York, Philadelphia and Washington DC are under consideration as bases for service representatives. The distances (in miles) among the cities are shown in the second table below. Formulate an ILP that will help Domino maximize its
annual profit.
|
|
Sales (in units)
|
|
Representative within 150 miles?
|
Yes
|
No
|
|
Boston
|
700
|
500
|
|
New York
|
1000
|
750
|
|
Philadelphia
|
900
|
700
|
|
Washington D.C.
|
800
|
450
|
|
Providence
|
400
|
200
|
|
Atlantic City
|
450
|
300
|
|
|
Distance (in miles)
|
|
|
Boston
|
N.Y.
|
Phil.
|
D.C.
|
|
Boston
|
0
|
222
|
310
|
441
|
|
New York
|
222
|
0
|
89
|
241
|
|
Philadelphia
|
310
|
89
|
0
|
146
|
|
Washington D.C.
|
441
|
241
|
146
|
0
|
|
Providence
|
47
|
186
|
255
|
376
|
|
Atlantic City
|
350
|
123
|
82
|
178
|