Question

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

Answer 1

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

Step-by-step 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