A farmer is preparing to plant a crop in the spring and needs to fertilize a field.  There are two brands of fertilizer to choose from, Super-gro and Crop-quick.  Each brand yields a specific amount of nitrogen and phosphate, as follows:

 

                   Nitrogen                Phosphate

                             (lb/bag)                 (lb/bag)       

Super-gro                 2                            4

Crop-quick               4                            3

 

The farmer’s field requires at least 16 pounds of nitrogen and 24 pounds of phosphate.  Super-gro cost $6 per bag, and Crop-quick cost $3 per bag.  The farmer wants to know how many bags of each brand to purchase in order to minimize the total cost of fertilizing.