A contractor, Susan Meyer, has to haul gravel to three building sites. She can purchase as much as 18 tons at a gravel pit in the north of the city and 14 tons at one in the south. She needs 10, 5, and 10 tons at sites 1, 2, and 3, respectively. The purchase price per ton at each gravel pit and the hauling cost per ton are given in the table below. Susan wishes to determine how much to haul from each pit to each site to minimize the total cost for purchasing and hauling gravel.

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A contractor, Susan Meyer, has to haul gravel to three building sites. She can purchase as much as 18 tons at a gravel pit in the north
of the city and 14 tons at one in the south. She needs 10, 5, and 10 tons at sites 1, 2, and 3, respectively. The purchase price per ton
at each gravel pit and the hauling cost per ton are given in the table below. Susan wishes to determine how much to haul from each pit
to each site to minimize the total cost for purchasing and hauling gravel.
Hauling Cost per Ton at Site
Pit
1
3
Price per Ton
North
$30
$60
$50
$100
South
$60
$30
$40
$120
Now suppose that trucks (and their drivers) need to be hired to do the hauling, where each truck can only be used to haul gravel from
a single pit to a single site. Each truck can haul 5 tons, and the cost per truck is five times the hauling cost per ton given above. Only
full trucks would be used to supply each site.
a. Formulate this problem as an assignment problem by constructing the appropriate cost table, including identifying the
assignees and tasks.
b. Find the optimal assignmen
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Transcribed Image Text:A contractor, Susan Meyer, has to haul gravel to three building sites. She can purchase as much as 18 tons at a gravel pit in the north of the city and 14 tons at one in the south. She needs 10, 5, and 10 tons at sites 1, 2, and 3, respectively. The purchase price per ton at each gravel pit and the hauling cost per ton are given in the table below. Susan wishes to determine how much to haul from each pit to each site to minimize the total cost for purchasing and hauling gravel. Hauling Cost per Ton at Site Pit 1 3 Price per Ton North $30 $60 $50 $100 South $60 $30 $40 $120 Now suppose that trucks (and their drivers) need to be hired to do the hauling, where each truck can only be used to haul gravel from a single pit to a single site. Each truck can haul 5 tons, and the cost per truck is five times the hauling cost per ton given above. Only full trucks would be used to supply each site. a. Formulate this problem as an assignment problem by constructing the appropriate cost table, including identifying the assignees and tasks. b. Find the optimal assignmen Attach File Browse Local Files Browse Content Collection
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