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 farmerís 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.