1. Four trucks are available to deliver milk to five groceries. The capacity and daily operating cost of each truck are shown in the following table.
Truck 1 2 3 4
Capacity (in gallons) 400 500 600 1,100
Daily operating cost ($) 45 50 55 60
The daily demands of each grocery are as follows: 100 gallons in grocery 1, 200 gallons in grocery 2, 300 gallons in grocery 3, 500 gallons in grocery 4, and 800 gallons in grocery 5.
The demand of each grocery store can be delivered by only one truck, but one truck may deliver to more than one grocery. Formulate an ILP that can be used to minimize the daily cost of meeting the demands of the five groceries.
2. 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
|