Question

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 $4100 million for the purchase of new aircraft to seat a total of 5100 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?

Answer 1

Let a, b, d represent the numbers of A330, B767, and B787 airplanes, respectively. The problem statement gives rise to 3 equations:
   250 a + 200 b + 250 d = 4100
   330 a + 270 b + 240 d = 5100
   2 a - b - d = 0

These can be solved by your favorite method* to give
   a = 6
   b = 8
   d = 4

You should buy 6 A330s, 8 B767s, and 4 B787s.


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* I find the matrix functions of my calculator are handy for solving sets of linear equations. If you want to do it by hand, you can use a = (b+d)/2. Then the equations simplify to
   13 b + 15 d = 164
   29 b + 27 d = 340
which can also be solved by any of your favorite methods to give
   (b, d) = (8, 4).

Answer 2

Let $x,y,z$ represent the numbers of $A330, B767,$ and $B787$ airplanes, respectively.

The equations are as follows

$250x + 200 y+ 250z = 4100$

$x + 270y + 240z = 5100$  

$2 x - y - z = 0$

solving these equations by matrix method calculator, we get  

$x = 6, y = 8,z = 4$

Therefore we should buy $6 A330s, 8 B767s,$ and $4 B787s.$