The Carbon coal company has 2 mines, a surface mine ad a deep mine. it costs $200 per day to operate the surface mine and $250 to operate the deep mine. Each mine produces a medium grade and a medium-hard grade coal, but in different proportions. This surface mine produces 12 tons of medium grade and 6 tons of medium-hard grade coal per day, and the deep mine produces 4 tons of medium grade and 8 tons of medium-hard grade coal every day. The company has a contract to deliver at least 600 tons of medium grade and 480 tons of medium-hard grade coal within 60 days. How many days should each mine be operated so that the contract can be filled at minimum cost

The company should operate the surface mine for 40 days and the deep mine for 30 days. Total costs = $15,500

Explanation:

we have to minimize the following equation: 200S + 250D

where:

S = surface mine

D = deep mine

the constraints are:

12S + 4D ≥ 600 (medium grade coal constraint)

6S + 8D ≥ 480 (medium hard coal constraint

S ≤ 60

D ≤ 60

S, D ≥ 0

S, D are integers

using solver, the optimal solution is 40S + 30D = $15,500

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you will have $2593.74 in 10 years if you set aside $1,000 at 10%

you will have $9321.91 in 20 years if you set aside $2000 at 8%

you will have $1469.32 in 5 years if you set aside $1000 at 8%

you will have $1296.87 in 10 years if you set aside $500 at 10%

you will have $239.66 in 15 years if you set aside $100 at 6%

you will have $4660.96 in 20 years if you set aside $1000 at 8%