Problem 1. A product is produced at three plants and shipped to three warehouses. The transportation costs per unit are shown in the following table:

 Warehouse Plant W1 W2 W3 Plant Capacity P1 20 16 24 300 P2 10 10 8 500 P3 12 18 10 100 Warehouse demand 200 400 300 

Requirements:

1. Write the complete mathematical model for this transportation problem.
2. Determine the optimal solution (e.g.: which plant should ship to which warehouse and the compute for the total (minimum) cost involved.

Problem 2. CarpetPlus sells and installs floor covering for commercial buildings. Brad Sweeney, a CarpetPlus account executive, was just awarded the contract for five jobs. Brad must now assign a CarpetPlus installation crew to each of the five jobs. Because the commission Brad will earn depends on the profit CarpetPlus makes. Brad would like to determine an assignment that will minimize total installation costs. Currently, five installation crews are available for assignment. Each crew is identified by a color code, which aids in tracking of job progress on a large white board. The following table shows the costs (in hundreds of dollars) for each crew to complete each of the five jobs:

 Job 1 2 3 4 5 Red 30 44 38 47 31 White 25 32 45 44 25 Crew Blue 23 40 37 39 29 Green 26 38 37 45 28 Brown 26 34 44 43 28 

Requirements:

1. Write the complete mathematical model for this assignment problem
2. Determine the optimal solution (e.g.: which installation crew should be assigned to which job and the compute for the total (minimum) cost involved.