Question 1: The Seaboard Trucking Company has expanded its shipping capacity by purchasing 120 trucks and trailers from a competitor that went bankrupt. The company subsequently located 40 of the purchased trucks at each of its shipping warehouses in Charlotte, Memphis, and Louisville. The company makes shipments from each of these warehouses to terminals in St. Louis, Atlanta and New York. Each truck is capable of making one shipment per week. The terminal managers have each indicated their capacity for extra shipments.
The manager at St. Louis can accommodate 40 additional per week, the manager at Atlanta can accommodate 60 additional trucks, and the manager at New York can accommodate 50 additional trucks. The company makes the following profit per truckload shipment from each warehouse to each terminal. The profits differ as a result of differences in products shipped, shipping costs, and transport rates.
|
Warehouse
|
|
St. Louis
|
Atlanta
|
New York
|
|
Charlotte
|
|
$1,800
|
2100
|
1600
|
|
Memphis
|
|
1000
|
700
|
900
|
|
Louisville
|
|
1400
|
800
|
2200
|
The company wants to know how many trucks to assign to each route to maximize profit. Formulate a linear programming model for this problem and solve it.
Question 2: A small metal-parts shop contains three machines- a drill press, a lathe, and a grinder- and has three operators, each certified to work on all three machines. However, each operator performs better on some machines than on others. The shop has contracted to do a big job that requires all three machines. The times required by the various operators to perform the required operations on each machine are summarized as follows:
|
Operator
|
Drill press
|
Lathe
|
Grinder
|
|
1
|
22
|
18
|
35
|
|
2
|
29
|
30
|
28
|
|
3
|
25
|
36
|
18
|
(time in minutes). The shop manager wants to assign one operator to each machine so that the total operating time for all three operators is minimized. Formulate and solve a linear programming model for this problem.