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.