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Everlong
King of the Neckbeards



Registered: 03/24/08
Posts: 9,087
Loc: Poconos
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Math Homework help? (Easy Algebra)
#11505415 - 11/22/09 04:40 PM (14 years, 5 months ago) |
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Hey, got some homework I've got trouble with. It involves solving systems of linear equations with three variables.
Suppose you are the Director of Purchasing for a large commercial airline company. Several years ago, anticipating significant growth in the air travel industry, you placed orders totaling $2100 million to purchase new aircraft that would seat a total of 4500 passengers. Some of the aircraft were Boeing 747s that cost $200 million each and seat 400 passengers and Boeing 777s that cost $160 million each and seat 300 passengers. Others were European Airbus A321s that cost $60 million and seat 200 passengers. At the time you were instructed to buy twice as many US manufactured aircraft as foreign aircraft.
a) Given the selection of three aircraft, how many of each type of aircraft did you order?
Due to recent poor economic conditions you have been told to alter the order for new equipment you made several years ago. The new aircraft had not been received and placed into service yet because of the long lead time to manufacture such complex and sophisticated equipment. The revised budget for the new aircraft is now $1810 million for 800 fewer total passenger seats. At this point in production Boeing charges $40 million for each 747 canceled and $35 million for each 777 aircraft canceled. In a similar fashion Airbus charges $20 million for each A321 aircraft canceled.
b) Given that all other criteria remain the same, how many of each type of aircraft did you cancel?
Part A I figured out.
200x + 160y + 60z = 2100 400x + 300y + 200z = 4500 X + Y - 2z = 0
Through elimination you get 5 of each.
I just have no clue what to do with Part B...
I figure you change the first two equations to
200x + 160y + 60z = 1810 400x + 300y + 200z = 3700
and I'm stuck there. Just don't know how to tie in the charges for canceling orders. Nothing I'm doing is coming out with logical answers.
Any help would be appreciated!
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Tedwilto
Veni, vidi, vici




Registered: 12/08/08
Posts: 5,158
Loc: Sunny Afternoon in
Last seen: 12 years, 9 months
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Re: Math Homework help? (Easy Algebra) [Re: Everlong]
#11528939 - 11/25/09 08:52 PM (14 years, 5 months ago) |
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Throw it into an augmented matrix and row reduce it down to echelon form. Thats what i would do with any question of this sort.
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