Let x represent the number of bags of brand A, y the number of bags of brand B.

The objective function is C=4x+5y (This represents the amount of nitrogen provided by a particular mix of fertilizers -- 4lbs from each A and 5 lbs from each B.)

The constraints are :

`4x+4y>=600` or `x+y>=150`

`2x+y<=250`

and the natural constraints `x,y>=0` .

The constraints form a bounded feasible region so the objective function has both a maximum and a minimum.

The maximum/minimum must occur at the boundary points which are (0,150),(0,250) and (100,50)

C(0,150)=750

C(0,250)=1250

C(100,50)=650

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Under the given restraints the maximum nitrogen is 1250lbs from 250 bags of brand B.

The minimum nitrogen is 650lbs from 100 bags of A and 50 bags of B

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The graph of the feasible region: