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PROBLEM 1
Table 1 A 1 : 100(50) = 5, B 1 : 100(20) = 2, B 2 : 50(30) = 1, C 2 : 50(40) = 2, C 3 : 50(50) = 2, Total: 13, A1: V 1 + W 1 = 50 0 + W 1 = 50 W 1 = 50 A2: V 1 + W 2 = 20 0 + W 2 = 20 W 2 = 20 B2: V 2 + W 2 = 30 V 2 + 20 = 30 V 2 = 10 B3: V 2 + W 3 = 40 10 + W 3 = 40 W 3 = 30 C3: V 3 + W 3 = 50 V 3 + 30 = 50 V 3 = 20 Unoccupied Cell: A 3 : 40-0-30 = 10 B 1 : 30-10-50 = - C 1 : 40-20-50 = - C 2 : 70-20-20 = 30 Table 2 A 1 : 200(20) = 4, B 1 : 100(30) = 3, B 2 : -50(30) = -1, C 2 : 50(40) = 2, C 3 : 50(50) = 2, Total: 10, A2: V 1 + W 2 = 20 0 + W 2 = 20 W 2 = 20 B1: V 2 + W 1 = 30 20 + W 1 = 30 W 1 = 10 B2: V 2 + W 2 = 30 V 2 + 20 = 30 V 2 = 10 B3: V 2 + W 3 = 40 10 + W 3 = 40 W 3 = 30 C3: V 3 + W 3 = 50 V 3 + 30 = 50 V 3 = 20 Unoccupied Cell: Transportation Cost:
Project
W arehouse 1 2 3 Supply
A 100
50
20 40
B
30
30
40
C
40 70
50
Demand 100 150 100 350
Project
Warehouse 1 2 3 Supply
A
50
20 40
B 100
30
30
40
C
40 70
50
Demand 100 150 100 350
Answer: The lowest possible transportation cost is 10,000.
2C = 100-100-200 = -
3A = 300-0-200 = 100
3B = 200-0-100 = 100
Table II Projects Warehouse A B C Supply 1 200 1, 300 200 1, 2 300 500 200 500 100 1,
300 200 1, 200 1, Demand 2,000 1,500 1,000 4, Transportation Cost: 1A: 1,500(200) = 300, 2A: 500(300) = 150, 2B: 500(200) = 100, 2C: 1,000(100) = 100, 3B: 1,000(200) = 200, Total 850, Value from the occupied cell: 1A: V1+W1=200; 0+W1=200; W1= 2A: V2+W1=300; V2+200=300; V2= 2B: V2+W2=200; 100+W2=200; W2=
2C: V2+W3=100; 100+W3=100; W3=
3B: V3+W2=200; 0+100=200; W3=
Unoccupied cell: 1B = 300-0-100 = 200 1C = 200-0-0 = 200 3A = 300-0-200 = 100 3C = 200-0-0 = 200 There are no negative evaluations. Therefore it is not possible to reduce the total cost of delivery. The lowest possible cost is 850,000.
Table 3.
- A 1 : 50-0-20 = 30 A 2 : 100(30) = 3,
- A 3 : 40-0-30 = 10 B 1 : 200(20) = 4,
- C 1 : 40-20-20 = 0 B 2 : -50(30) = -1,
- C 2 : 70-20-20 = 30 C 2 : 50(40) = 2,
- C 3 : 50(50) = 2,
- Total: 10,
- Laguna,1 4,000 5 60 55 4, From/To Manila (A) Quezon City (B) Caloocan City (C) Supply
- Batangas,2 500 65 3000 60 66 3,
- Mindoro,3 500 74 80 2000 75 2,
- Demand 5,000 3,000 2,000 10,000=10,
- A1: 4000 (5) = 20, Total Cost:
- A2: 500 (65) = 32,
- A3: 500 (74) = 37,
- B2: 3000 (60) = 180,
- C3: 2000 (750) = 150,
- TOTAL COST= P419,
- A1: V1+W1= 5, W1= Value from the occupied cell:
- A2: V2+W1= 65, V2=
- A3:V3+W1= 74, V3=
- B2: V2+W1= 60, V2=
- C3: V3+W3= 75, V3 =
- B1: 60-0-46= Unoccupied cell
- C2: 66-60-29=-
- C1: 55-0-46=
- B3: 80-14-1=
- The lowest transportation cost of Aling Miling is P419,
