In 2001, 400 seat Boeing 747s were priced at $200 million each, 300 seat Boeing 777s were priced at $160 million, and 200 passenger Airbus A321s were priced at $60 million. Suppose you were the purchasing manager of an airline company and had a $2100 million budget to purchase new aircraft to seat a total of 4500 passengers. Your company has a policy of supporting U.S. industries, and you have been instructed to purchase twice as many Boeing planes as Airbus planes. How much of each of the three planes (747, 777, and A321) should you order? (Please show all work)
a.) Identify the three variables.
c.) Solve your system using the Gauss-Jordan elimination matrix method.
a) Let x, y, z be the number of planes which should be orders for 400 seat Boeing 747s, 300 seat Boeing 777s and 200 passenger Airbus A321s respectively.
b) So the system of equations is
400x+300y+200z=4500 --- (1)
200x+160y+60z = 2100 --- (2)
x + y = 2z --- (3) ...
The solution gives detailed steps on setting and solving linear system of equations using the example of plane order. A Gauss-Jordan elimination matrix method is used in steps.