To determine which location will cost the least for mining and reclamation at the end of the mining period, we need to calculate the total cost for each location by summing the cost of land, cost of equipment, and the cost incurred due to the daily mining and reclamation over the entire period of days.
Let's go through the calculations step-by-step for each location:
Location 1:
- Cost of land: \[tex]$100,000
- Cost of equipment: \$[/tex]10,000
- Daily cost of mining and reclamation: \[tex]$5,000
- Number of days: 30
The total cost for Location 1:
\[
\text{Total cost for Location 1} = \$[/tex]100,000 + \[tex]$10,000 + (\$[/tex]5,000 \times 30) = \[tex]$100,000 + \$[/tex]10,000 + \[tex]$150,000 = \$[/tex]260,000
\]
Location 2:
- Cost of land: \[tex]$35,000
- Cost of equipment: \$[/tex]6,000
- Daily cost of mining and reclamation: \[tex]$4,500
- Number of days: 45
The total cost for Location 2:
\[
\text{Total cost for Location 2} = \$[/tex]35,000 + \[tex]$6,000 + (\$[/tex]4,500 \times 45) = \[tex]$35,000 + \$[/tex]6,000 + \[tex]$202,500 = \$[/tex]243,500
\]
Location 3:
- Cost of land: \[tex]$30,000
- Cost of equipment: \$[/tex]7,500
- Daily cost of mining and reclamation: \[tex]$3,500
- Number of days: 120
The total cost for Location 3:
\[
\text{Total cost for Location 3} = \$[/tex]30,000 + \[tex]$7,500 + (\$[/tex]3,500 \times 120) = \[tex]$30,000 + \$[/tex]7,500 + \[tex]$420,000 = \$[/tex]457,500
\]
Location 4:
- Cost of land: \[tex]$40,500
- Cost of equipment: \$[/tex]8,000
- Daily cost of mining and reclamation: \[tex]$7,000
- Number of days: 65
The total cost for Location 4:
\[
\text{Total cost for Location 4} = \$[/tex]40,500 + \[tex]$8,000 + (\$[/tex]7,000 \times 65) = \[tex]$40,500 + \$[/tex]8,000 + \[tex]$455,000 = \$[/tex]503,500
\]
Now, we compare the total costs of all four locations:
- Location 1: \[tex]$260,000
- Location 2: \$[/tex]243,500
- Location 3: \[tex]$457,500
- Location 4: \$[/tex]503,500
The least total cost is \$243,500, which corresponds to Location 2.
Therefore, the location that will cost the least for mining and reclamation at the end of the mining period is:
Location 2.
