Due to heavy rains that destroyed numerous roadways in Jamaica the National Works Agency (NWA) has decided to repair 300 km of the Sothern Coastal Highway and 200 km of Type A roads from Kingston to Lucea. The repair will cost $2 million per km for the Type A roads and $8 million per km for the Southern Coastal Highway. The NWA has identified two firms China Harbour and Caribbean Construction. Caribbean Construction can repair at most 300 km while China Harbour has no restriction on the amount of roadway it can repair. Each company must be awarded a contract of at least $300 million (before discounts). Each company wants to maximize the quantity of highway and Type A roads awarded by the NWA so are willing to offer a per km discount. China Harbour offers a discount of 1% for each km of Southern Coastal Highway and Type A road. Caribbean Construction offers a flat discount of $30,000 for each km of Type A road and $50,000 for each km of the Southern Coastal Highway. Due to a significant budget shortage the NWA wants to maximize the total discount received from the two companies. Let x and y represent the number of kilometres of Type A roads and Southern Coastal Highway.
Due to heavy rains that destroyed numerous roadways in Jamaica the National Works Agency (NWA) has decided to repair 300 km of the Sothern Coastal Highway and 200 km of Type A roads from Kingston to Lucea. The repair will cost $2 million per km for the Type A roads and $8 million per km for the Southern Coastal Highway. The NWA has identified two firms China Harbour and Caribbean Construction. Caribbean Construction can repair at most 300 km while China Harbour has no restriction on the amount of roadway it can repair. Each company must be awarded a contract of at least $300 million (before discounts).
Each company wants to maximize the quantity of highway and Type A roads awarded by the NWA so are willing to offer a per km discount. China Harbour offers a discount of 1% for each km of Southern Coastal Highway and Type A road. Caribbean Construction offers a flat discount of $30,000 for each km of Type A road and $50,000 for each km of the Southern Coastal
Highway. Due to a significant budget shortage the NWA wants to maximize the total discount received from the two companies. Let x and y represent the number of kilometres of Type A roads and Southern Coastal Highway.
We know
- Total Type A Road to be repaired = 200km
- Total South Coast to be repaired = 300km
Let the amount of Type A and South Coast repaired by China be X and Y respectively
- X = Amount of Type A repaired by China
- Y = Amount of South Coast repaired by China
So the amount repaired by Caribbean would be
- 200 - X = Amount of Type A repaired by Caribbean
- 300 - Y = Amount of South Coast repaired by Caribbean
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