A company has three factories A, B and C which supply units to warehouses X, Y and Z every month. The capacities of the factories are 60, 70 and 80 units at A, B and C respectively. The requirements of X, Y and Z per month are 50, 80 and 80 units respectively. Transportation costs per unit in ringgits are given in the following table. How many units should ship from each factory so that the total cost is minimum? Use VAM method for the initial solution and Stepping Stone method to obtain an optimal solution.
|
Factories
|
Warehouses
|
|
X
|
Y
|
Z
|
|
A
|
8
|
7
|
5
|
|
B
|
6
|
8
|
9
|
|
C
|
9
|
6
|
5
|
The Dean of the Faculty of Science at City Science University has decided to
apply the Hungarian method in assigning lecturers to courses for the next semester. As a criterion for judging who should teach each course, the Dean reviews the past two years' teaching evaluations (which were filled out by students). Since each of the four lecturers taught each of the four courses at one time or another during the two-year period, the Dean is able to record a course rating for each lecturer. These ratings are shown in the table below. Find the best assignment of lecturers to courses to maximize the overall teaching rating.
|
Lecturer
|
Biology
|
Chemistry
|
Physics
|
Applied Sciences
|
|
Nora Bee
|
90
|
65
|
95
|
40
|
|
Lee Along
|
70
|
60
|
80
|
75
|
|
Rama Sundar
|
85
|
40
|
80
|
60
|
|
Charles Abby
|
55
|
80
|
65
|
55
|