Winston Chapter 7.1, Page 350, Number 6 (Transportation)

Problem Statement: A bank has two sites at which checks are processed. Site 1 can process 10,000 checks per day, and site 2 can process 6,000 checks per day. The bank processes three types of checks: vendor, salary, and personal. The processing cost per check depends on the site (see Table 4). Each day, 5,000 checks of each type must be processed. Formulate a balanced transportation problem to minimize the daily cost of processing checks.

Table 4: Costs based on check type and site.
| |Check Type |Site 1 |Site 2 |
| |Vendor checks |$0.05 |$0.03 |
| |Salary checks |$0.04 |$0.04 |
| |Personal checks |$0.02 |$0.05 |

Questions:
A. Represent the problem graphically.
B. Formulate the problem mathematically and use LP Simplex option of the Quant software to solve it. Print the input and output of the Quant.
C. Create the balanced transportation tableau.
D. Find the initial basic feasible solution using the Northwest Corner Method.
E. Find the initial basic feasible solution using the Minimum Cost Method.
F. Use the solution on part D and perform Transportation Simplex Method to find the optimal solution.
G. Write a report explaining the optimal solution.

Answers:
A. The problem is represented graphically. The site locations listed on the left-hand side circles on the graph represent supply points. The right-hand side circles on the graph represent demand points. Each of the points has its capacity listed below itself. Each line between a supply and demand point represents a possible shipment. The cost per