A contractor, Susan Meyer, has to haul gravel to three building sites. She can p

Question

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.

Hauling Cost per Ton at Site

Pitt

1

2

3

Price per Ton

North

$30

$60

$50

$100

South

60

30

40

120

Susan wishes to determine how much to haul from each pit to each site to minimize the total cost for purchasing and hauling gravel. Formulate and solve a spreadsheet model for this problem.

Hauling Cost per Ton at Site

Pitt

1

2

3

Price per Ton

North

$30

$60

$50

$100

South

60

30

40

120

Explanation / Answer

Soltion is minimum cost is $3570 as follow

Working

1. Total Cost from North is as follow

2. Total Cost from South is as follow

3. Now the differnce of these cost are as follow

4. Prioritising the requirement based upo limited qty of 18tonnes from North & 14 Tonnes from South

Pitt Purchase from Qty Cost Total Cost 1 North 10 130 1300 2 South 5 150 750 3 South 2 160 320 3 North 8 150 1200 Total 25 3570

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