Formulate the situation as a system of linear equations. Be sureto state clearly the meaning of each variable. Solve using theGauss-Jordan method. State your final answer in terms of theoriginal question. (If the system is inconsistent, answerINCONSISTENT. If the system is dependent, parametrize the solutionsin terms of the parameters u and v.)
A large commercial farm needs 38,000 pounds of potash, 73,000pounds of nitrogen, and 27,000 pounds of phosphoric acid. Threebrands of fertilizer, GrowRite, MiracleMix, and GreatGreen, areavailable and contain the amounts of potash, nitrogen, andphosphoric acid per truckload listed in the table. How manytruckloads of each brand should be used to provide the requiredpotash, 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 | 1600 |
| Phosphoricacid | 300 | 400 | 500 |
