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.
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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
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