Solve the following transportation linear programming model using VAM and MODI.
Minimize f = 14x1A + 49x1B + 60x1C + 50x2A + 60x2B + 65x2C + 45x3A + 53x3B + 63x3C
Subject to x1A + x1B + x1C = 14 x1A + x2A + x3A = 20
x2A + x2B + x2C = 14 x1B + x2B + x3B = 15
x3A + x3B + x3C = 27 x1C + x2C + x3C = 30
Establish the initial feasible solutions of the LP model one for each of the NCR, MCM, and VAM. Then, apply MODI to determine the optimal solution.
Minimize f = 3x1A + 14x1B + 8x1C + 7x2A + 9x2B + 5x2C + 4x3A + 6x3B + 12x3C
Subject to x1A + x1B + x1C = 20 x1A + x2A + x3A = 25
x2A + x2B + x2C = 40 x1B + x2B + x3B = 30
x3A + x3B + x3C = 30 x1C + x2C + x3C = 35
Binas Enterprises manufactures the central processing unit (CPU) for a line of personal computers. The CPUs are manufactured in Makati City, Taguig City and Quezon City and transported to warehouses in Pasay City, Cavite, Dagupan, Cebu, and Davao for further distribution. The following table shows the number of CPUs available at each plant, the number of CPUs required by each warehouse, and the transportation costs (pesos per unit).
Plant
Warehouse
Pasay City
Cavite
Dagupan
Cebu
Davao
CPUs Available
Makati City
5
4
9
15
20
4000
Taguig City
6
7
15
21
28
9000
Quezon City
9
11
13
21
30
8000
CPUs Required
3000
5000
4000
6000
3000
21000
Develop a network representation of the distribution system (transportation problem).
Determine the amount that should be shipped from each plant to each warehouse to minimize the total transportation cost.
A company has six managers available for work on six separate projects and only one manager can work on one project. The cost (in thousands of pesos) of assigning each manager to each project is given in the following table. The objective is to assign managers to projects such that the total cost of assignment is at a minimum.
Managers
Projects
Mercury
Venus
Mars
Jupiter
Saturn
Uranus
Ms. Laguerta
29
27
20
18
21
24
Ms….