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.
Required:
a. Write out a linear programming model to minimize the operating costs of the mining fields and decide how many days the company needs to operate each of these fields?

Minimize Z : 55000x1+45000y1

250x1 +200y1 >= 120000

300 x1+ 450 y1 >= 170000

where x1,y1 <= 0

Explanation:

As mentioned in the question

A. As a matter of minimization, a linear programming model will be used.

Assume x1 and y1 are the units generated in field A and field B.

The  Minimize Z function can be written as:-

Z : 55000x1+45000y 1

According to the linear programming model, the  Subject to the limits can be written as

250x1 +200y1 >= 120000

300 x1+ 450 y1 >= 170000

where x1,y1 <= 0

the answer would be voluntary exchange -

"the act of buyers and sellers freely and willingly engaging in market transactions. moreover, transactions are made in such a way that both the buyer and the seller are better off after the exchange than before it occurred."

hope this : )

-shy