Define your variables and set up the system of equations that would solve the pr

Question

Define your variables and set up the system of equations that would solve the problem.

Boeing 747s seat 400 passengers and are priced at $200 million each, Boeing 777s seat 300 passengers and are priced at $160 million, and European Airbus A321s seat 200 passengers and are priced at $60 million. You are the purchasing manager of an airline company and have a $6,180 million budget to purchase new aircraft to seat a total of 13,200 passengers. Your company has a policy of supporting U.S. industries, and you have been instructed to buy twice as many U.S.- manufactured aircraft as foreign aircraft. Given the selection of three aircraft, how many of each should you order?

Explanation / Answer

Let 747s purchased =x;

Let 777s purchased =y;

Let A321s purchased =z;

Given;

x+y = 2z --------------------------------------------1   (you have been instructed to buy twice as many U.S.- manufactured aircraft as foreign aircraft)

and 400x + 300y +200z = 13200 --------------------------------------2 (total passengers = 13200)

and 200x + 160 y + 60z = 6180 ----------------------------------3 (total cost = 6180 million)

Solving from 1,2 and 3, we get x =12, y =18, z=15.

hence no. of 747s = 12

no. of 777s = 18

no. of A321s = 15

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