Formulate the situation as a system of linear equations. Be sure to state clearly the meaning of each variable. Solve using the Gauss-Jordan method. State your final answer in terms of the original question. (If the system is inconsistent, answer INCONSISTENT. If the system is dependent, parametrize the solutions in terms of the parameters u and v.)

A large commercial farm needs 30,000 pounds of potash, 60,500 pounds of nitrogen, and 21,500 pounds of phosphoric acid. Three brands of fertilizer, GrowRite, MiracleMix, and GreatGreen, are available and contain the amounts of potash, nitrogen, and phosphoric acid per truckload listed in the table. How many truckloads of each brand should be used to provide the required potash, nitrogen, and phosphoric acid?

x₁= truckloads of GrowRite

x₂= truckloads of MiracleMix

x₃= truckloads of GreatGreen

(Pounds per

truckload) GrowRite MiracleMix GreatGreen

Potash 400 600 700

Nitrogen 500 1000 160

Phosphoric

acid 300 400 500