Cities A and B produce 50 tons and 40 tons of waste per day, respectively. Waste must be incinerated at incinerator 1 or 2, and each incinerator can process up to 60 tons of waste per day. The cost to incinerate waste is $300/ton at incinerator 1 and $200 at incinerator 2.

Incinerator reduces each ton of waste to .2 tons of debris, which must be dumped at one of two landfills. Each landfill can receive at most 20 tons of debris per day. It costs $2/mile to transport a ton of material (debris or waste). Distance between locations are shown below

Distance |
Incinerator 1 |
Incinerator 2 |

City A |
10 |
5 |

City B |
12 |
14 |

Distance |
Landfill 1 |
Landfill 2 |

Incinerator 1 |
5 |
8 |

Incinerator 2 |
9 |
6 |

Formulate a LP model to minimize the total cost of disposing of the waste in both cities.

#1) Decision Variable

Let = tons of City I waste that is sent to Incinerator j (i=A,B and j=1,2)

Let = tons of debris sent from incinerator I to landfill j (i=1,2 and j=1,2)

#2) Objective Function:

#3) Constraints:

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