Two mining fields, Field A and Field B, of a coal mining company produce Lignite and Bituminous coal. The operating cost per day for Field A and Field B are $55,000 and $45,000, respectively. The recent records at the company indicate that Field A can produce 250 tons of Lignite along with 300 tons of Bituminous coal per day, whereas Field B can produce 200 tons of Lignite along with 450 tons of Bituminous coal per day. The expected demands to be met are 120,000 tons of Lignite and 170,000 tons of Bituminous coal. Leadership wants to minimize the operating costs of the mining fields. Assuming A and B represent number of days Field A and Field B operates respectively. Which equation indicates constraint on the capacity of the Bituminous coal?

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anthougo anthougo · Answer 2 · 2021-12-27T06:01:08+01:00

The equation indicating the constraint on the Bituminous coal's capacity is 300A + 450B ≥ 170,000.

Data and Calculations:

Field A Field B

Operating costs per day $55,000 $45,000

Lignite coal per day (tons) 250 200

Bituminous coal per day (tons) 300 450

Number of days of operation A B

Expected demand:

Lignite coal = 120,000 tons

Bituminous coal = 170,000 tons

Constraint on the capacity of the Bituminous coal = 300A + 450B ≥ 170,000

Where:

A = the operational days of Field A, which minimizes costs

B = the operational days of Field B, which minimizes costs

Thus, the equation that indicates the constraint on the capacity of the Bituminous coal is 300A + 450B ≥ 170,000.

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