In Example 2, we saw that Airbus A330-300s seat 330 passengers and cost $250 million each, Boeing 767-300ERs seat 270 passengers and cost $200 million each, while Boeing Dreamliner 787-9s seat 240 passengers and cost $250 million each. You are the purchasing manager of an airline company and have a spending goal of $5550 million for the purchase of new aircraft to seat a total of 6750 passengers. Your company has a policy of supporting U. S. industries, and you have been instructed to buy twice as many Boeings as Airbuses. Given the selection of three aircraft, how many of each should you order? Airbus A330-300s

Boeing 767-300ERs

Boeing Dreamliner 787-9s

9514 1404 393

Step-by-step explanation:

Let x, y, z represent the numbers of A330, B767, and B787 aircraft to order, respectively. The problem statement suggests 3 equations:

  330x +270y +240z = 6750 . . . . . total seats

  250x +200y +250z = 5550 . . . . . total cost (millions)

  2x -y -z = 0 . . . . . . . . . . . . . . . . . . . ratio of orders

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These can be solved by a variety of methods, including on-line equation solvers. If you want to do it by hand, substitution can help.

First divide by common factors:

  11x +9y +8z = 225

  5x +4y +5z = 111

Write an expression for z and substitute:

  z = 2x -y

  11x +9y +8(2x -y) = 225   ⇒   27x +y = 225

  5x +4y +5(2x -y) = 111   ⇒   15x -y = 111

Adding the second of these to the first gives ...

  (27x +y) +(15x -y) = (225) +(111)

  42x = 336 . . . simplify

  x = 8 . . . . . . . . divide by 42

  15(8) -111 = y = 9

  z = 2(8) -9 = 7

The solution to the equations is (x, y, z) = (8, 9, 7).

The order should be for 8 A330s, 9 B767s, and 7 B787s.