A company manufactures the product in two cities, which are Dallas and Houston. The daily production capacities at the Dallas and Houston are 160 and 200, respectively. Products are shipped through air to customers in San Francisco and New York. The customers in each city need 140 units of product per day. Because of deregulation of air fares, the company thinks that it might be cheaper to first fly some products to Chicago or Los Angeles and then fly the products to their final destinations. The costs of flying one unit of product between these cities are given in table below.
| |
|
|
TO |
|
|
|
| FROM |
Dallas |
Houston |
Chicago |
LA |
Frisco |
NYC |
| Dallas |
0 |
xxx |
9 |
14 |
26 |
29 |
| Houston |
xxx |
0 |
16 |
13 |
27 |
26 |
| Chicago |
xxx |
xxx |
0 |
7 |
17 |
18 |
| LA |
xxx |
xxx |
7 |
0 |
15 |
17 |
| Frisco |
xxx |
xxx |
xxx |
xxx |
0 |
xxx |
| NYC |
xxx |
xxx |
xxx |
xxx |
xxx |
0 |
The company wants to reduce the total cost of daily shipments of required products to its customers.
Mention the goal function and constraints for problem.
Find out the optimum solution for problem.