Question
The XYZ Construction company won a bidding to supply cements to three different horizontal (road) projects. Project 1, 2, and 3 require 100 bags, 170 bags, and 180 bags, respectively. It has three warehouses: A, B, and C. The available bags per warehouse are as follows: 120 bags for A, 180 bags for B, and 150 bags for C. It will cost P50/bag to transport from warehouse A to Project 1, P20/bag to Project 2, P40/bag to Project 3; warehouse B cost P30, P50, and P40, respectively for Project 1, 2 and 3; P40, P30, P20 for warehouse C. Assign number of bags from each warehouse to its corresponding Project that will minimize the cost of transportation.
Answers
GPT 3.5
To minimize the cost of transportation, we need to assign the bags in the warehouses to their corresponding projects in the most cost-effective way. We can do this by finding the minimum cost for each project.
For Project 1:
- From Warehouse A: We can transport a maximum of 120 bags. The cost is 120 * P50/bag = P6000.
- From Warehouse B: We can transport a maximum of 100 bags. The cost is 100 * P30/bag = P3000.
- From Warehouse C: We can transport a maximum of 100 bags. The cost is 100 * P40/bag = P4000.
The minimum cost for Project 1 is P3000 from Warehouse B.
For Project 2:
- From Warehouse A: We can transport a maximum of 170 bags. The cost is 170 * P20/bag = P3400.
- From Warehouse B: We can transport a maximum of 170 bags. The cost is 170 * P50/bag = P8500.
- From Warehouse C: We can transport a maximum of 170 bags. The cost is 170 * P30/bag = P5100.
The minimum cost for Project 2 is P3400 from Warehouse A.
For Project 3:
- From Warehouse A: We can transport a maximum of 150 bags. The cost is 150 * P40/bag = P6000.
- From Warehouse B: We can transport a maximum of 180 bags. The cost is 180 * P40/bag = P7200.
- From Warehouse C: We can transport a maximum of 180 bags. The cost is 180 * P20/bag = P3600.
The minimum cost for Project 3 is P3600 from Warehouse C.
Therefore, the optimal assignment of bags from each warehouse to its corresponding project is as follows:
- Project 1: 100 bags from Warehouse B
- Project 2: 170 bags from Warehouse A
- Project 3: 180 bags from Warehouse C
For Project 1:
- From Warehouse A: We can transport a maximum of 120 bags. The cost is 120 * P50/bag = P6000.
- From Warehouse B: We can transport a maximum of 100 bags. The cost is 100 * P30/bag = P3000.
- From Warehouse C: We can transport a maximum of 100 bags. The cost is 100 * P40/bag = P4000.
The minimum cost for Project 1 is P3000 from Warehouse B.
For Project 2:
- From Warehouse A: We can transport a maximum of 170 bags. The cost is 170 * P20/bag = P3400.
- From Warehouse B: We can transport a maximum of 170 bags. The cost is 170 * P50/bag = P8500.
- From Warehouse C: We can transport a maximum of 170 bags. The cost is 170 * P30/bag = P5100.
The minimum cost for Project 2 is P3400 from Warehouse A.
For Project 3:
- From Warehouse A: We can transport a maximum of 150 bags. The cost is 150 * P40/bag = P6000.
- From Warehouse B: We can transport a maximum of 180 bags. The cost is 180 * P40/bag = P7200.
- From Warehouse C: We can transport a maximum of 180 bags. The cost is 180 * P20/bag = P3600.
The minimum cost for Project 3 is P3600 from Warehouse C.
Therefore, the optimal assignment of bags from each warehouse to its corresponding project is as follows:
- Project 1: 100 bags from Warehouse B
- Project 2: 170 bags from Warehouse A
- Project 3: 180 bags from Warehouse C